I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public.

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Abstract
The operation of a large and complex electric power system requires meticulous and rigorous study and incessant planning. All the players involved, must plan ahead to account for the uncertainties that can affect the hour-to-hour, day-to-day, medium-term and long-term supply of electricity. Mediumterm operations and planning provides the players with guidelines and strategies for short-term operating decisions vis-à-vis the market. Adequate planning helps the players to mitigate or be prepared for unforeseen circumstances encountered during scheduling of electricity generation at any stage. This thesis focuses on some aspects of the least explored medium-term operations and planning issues in power systems in the deregulated electricity market environment. The issues addressed in the thesis are diverse but inter-linked as medium-term problems, which have surfaced due to deregulation or are outcomes of unique thought-processes emerging from the restructuring phenomenon. The thesis presents a novel approach to security coordinated maintenance scheduling in deregulation wherein the ISO does not generate a maintenance schedule by itself, but assesses the maintenance schedules from individual gencos by incorporating them in a medium-term security constrained production scheduling model, and verifying whether they result in unserved energy at one or more buses. Based on the information on bus-wise unserved energy, the ISO generates corrective signals for the genco(s), and directs them to alter their maintenance schedules in specific periods and re-submit. The proposed scheme exploits the concept of commons and domains to derive a novel factor to allocate the unserved energy at a bus to a set of generators responsible. The coordination scheme is based on individual genco’s accountability to unserved energy at a bus. Another important question addressed in the thesis is whether there is a need to consider customer’s locations in the power system when the utility provides service to them. In other words, whether the reliability of the load service provided by the utility varies across the system, from bus to bus, and if so, how are the Locational Marginal Prices (LMPs), which are determined from market auctions, affected by such variations. The thesis also answers the important question of how the LMPs can be differentiated by the Load Service Probability (LSP) at a particular location, so that it is fair to all customers. A new approach to determining the bus-wise LSP indices in power systems is proposed in the thesis. These LSP indices are arrived at by defining and computing bus-wise Loss of Load Probability (LOLP) indices. The discrepancy in LMPs with respect to the bus-wise LSP is then

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without overloading the transmission system. The Feasibility Set helps in limiting the type and number of reinforcement options available to the transmission planner in selected existing corridors.
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.the Decomposition Approach and the Unified Approach are proposed to solve the TRP optimization problem. Two different solution approaches. engineering judgement.investigated and the bus-wise LSP indices are thereafter utilized to formulate a novel proposition for LSP-differentiated LMPs for electricity markets. experience and thumb-rules to construct a Feasibility Set. The thesis furthermore addresses the medium-term Transmission Reinforcement Planning (TRP) problem and proposes a practical approach to TRP by making use of standard design practices. Mathematical optimization procedure is then applied considering the Feasibility Set. to attain an optimal set of reinforcement decisions that are economical and meets the system demand in the medium-term.

guidance and patience during the course of my PhD studies. Ismael. I would like to thank my colleagues and friends. Hassan. I also extend my hearty appreciation to my wife Nilam for her understanding and support. I also thank Professors Claudio Canizares. for their support and co-operation. I also thank Mr. I don’t have any words to acknowledge the contribution of my loving kids Jay and Jeet to my PhD thesis. Gannaya Bommali for making my stay very friendly and pleasant. that she is with me and will shower her blessings to motivate and encourage me. Shesha Jayaram and Miguel Anjos. I will never ever forget that it has cost a lot to reach where I am today. Mohammed. to see me prosper. as always. Deepak. at the cost of her life. Rafael.Acknowledgements
I take this opportunity to thank my research supervisor Professor Kankar Bhattacharya for his invaluable support. University of Waterloo. Behnam and Tarek for maintaining an interesting research environment in the lab. Steve. My father also has suffered a lot in his life without letting me know. I acknowledge the financial support received from Natural Sciences and Engineering Research Council of Canada and the Ontario Graduate Scholarship in Science and Technology. Lianxi. Amir. It is my parents’ years of love and affection that I am submitting my PhD thesis on this day. and has always encouraged me. I thank Professor Jatin Nathwani for his moral support and motivation. Electrical and Computer Engineering Department. Hossein. in the Electricity Market Simulation and Optimization Lab at the ECE Department: Hamid. Mingbo. Chaomin. I wish my mother to be present when I defend my thesis and I know. I would like to express my sincere gratitude towards my mother for all scarifies she made. Sumit. I also acknowledge the cooperation received from all the staff members of the Office of Graduate Studies. Ayed.
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. % Susceptance. Peak) Index for hydro generating units in a genco Index for the set of all hydro units in the system Index for generating units within a genco Set of generating units connected to the same bus i Set of generator buses (kL Є K) supplying load bus. $/MW No-load generation cost of a generating unit. m Index for reinforcement option Set of commons Index for period (in this work. j b h H k K kL KU l L m N1 o p
t
Index for system buses Index for sub-periods of a period (Base. t = 1. when unserved energy is maximum Set of buses that have unserved power in period. a period represents a month. $/h Start-up cost of a generating unit. $/MWh Quadratic component of generator cost characteristics. 12) Set of generating companies (gencos) Set of gencos receiving corrective signal from ISO.. u∈U
U u Constants: Aux B Cg CgA CgB Cg
C
Auxiliary consumption of a generating unit. $/MWh xiii
Cgq Cm Cc Cs Cn
.. $/h Linear component of generator cost characteristics. $/MVAr2 Maintenance cost of a generating unit. $/MW2/h Reactive power generation cost. $ Cost of unserved energy.U. L Set of all generating units in the system Index for line voltage class (110 kV. Intermediate. Generator operating cost. 220 kV. P. 500 kV) Load buses in the system (L Є i) Index for a specific period in t.Nomenclature and Acronyms
Sets and Indices: i. $/MWh Fixed component of generator cost characteristics.

u Minimum reactive capacity of a support unit in MVAr or p.u Line charging admittance. % Conductance. MW or p. MW xiv
. MW or p.u Maximum capacity of a generating unit.u
Min
LF LSF N Nl Ng No NM PMax PD Pg Pg T T1 ρ QcMax Qc QD QgMax QgMin V
Max Min Max Min
RSV
V
Ych Parameters AC C CPROB MCAPu
Absolute contribution of generator.u Total power demand in the system. h Duration of maintenance for a unit.E G I
Max
Hydro energy availability factor for a hydro unit. p.u Relative contribution of generator g Cumulative probability of Outage Capacity of u on maintenance in m.u Maximum reactive capacity of a generating unit in MVAr or p.u Minimum reactive capacity of a generating unit in MVAr or p. p.u Minimum capacity of a generating unit.u Maximum permissible voltage at a bus. over a year Medium-term forecast of electricity price.u Minimum permissible voltage at a bus. MW Duration of sub-period b. p.u System reserve requirement. $/MWh Maximum reactive capacity of a support unit in MVAr or p. p. MW or p.u Transmission line loss factor.u Reactive power demand in MVAr or p. p. p. % Load Scaling Factor Total number of system buses Total number of load buses Total number of generator buses Total number of reinforcement options Number of units on simultaneous maintenance Power transfer capacity of a line.u Line thermal capacity. MW or p.

Table 1. gathers paramount importance in view of the complexities in securing funds to undertake large power projects for capacity addition [1-3]. In the context of deregulation. unit commitment Economic load dispatch. in the context of vertically integrated power industry structure. Tackle faults.1 provides an overview of the various activities of the power system operator and the system planner from real-time operation to 10-years in advance. load curtailment. load flow. For example. frequency regulation. many of these activities have undergone a paradigm shift. production scheduling Schedule hydro reservoir drawdown.1 Introduction
The electric power sector has come a long way since the early years of small power generating stations to the present day giant power stations of large capacities and interconnected extra high voltage transmission networks.Chapter 1 Introduction to Medium-Term Operation and Planning in Power Systems
1. capacitor switching. disturbances. the aspect of longterm planning has been affected significantly after the onset of deregulation. capacitor citing and sizing (reactive power planning).1 Power System Operations and Planning in Time-Domain Time-frame > 10 years ahead 1 – 5 years ahead 1 – 2 years ahead 1 – 7 days ahead 5 – 30 minutes ahead 1 – 300 seconds Activity Planning to expand the generation & transmission system to meet the demand Planning for fuel supply contracts. Table-1. Power system operations and planning activities can be classified into various categories depending on the time-horizon of the activity and the decision variables involved [4]. short-circuits. transmission reinforcement planning Generating unit maintenance schedules. etc. Finding out suitable strategies for efficient power system operation and planning on a utility-wide scale through the formation of interconnected grids. oscillations Referred to asLong-term planning Medium-term planning Medium-term operations Short-term operations Real-time operations Transient and dynamic state operations
1
.

operation and maintenance of the units. operations and maintenance. the term operations and planning have often been used together or interchangeably since these cover a wide range of overlapping functions. the utility’s activities in the time-frame of 1-2 years ahead. In the erstwhile vertically integrated utility structure. transportation and allocation schedules are also combined with medium-term operation activities of the utilities [5]. referred to as medium-term. while planning activities are those where new investment decisions are the outcomes. medium-term operations and planning. responsible for all generation in the utility. the Central Load Dispatch Centre (CLDC) interacted with the “power generation division” (denoted by G. responsible for all transmission) and the “distribution division” (denoted by D.capacitor citing and sizing. To clearly distinguish between operations and planning activities in the context of this thesis. developed the medium.and long-term plans for the system as a whole. and may include reactive power planning.). This is usually combined with medium-term production scheduling. and using its own forecast of demand growth. Both operations and planning activities are present in this time horizon. where gross production schedules are drawn up one or two years in advance taking into consideration aggregated load duration curves (LDC) and hydro energy allocation schedules for reservoir-based hydro units. responsible for all low voltage networks). coordination and hierarchical functions of utility operations and planning across different entities / players. operations activities are those where production schedules are drawn up. In some cases.1. The medium-term operation activities include generating unit maintenance scheduling.As may be noted from Table-1. transmission reinforcement planning. are quite extensive and involving.1 shows the basic linkages of information flow. procurement. fuel production. Fig. etc. the “transmission division” (denoted by T. both in the context of deregulation (on the left) and in a vertically integrated environment (on the right). The central planner received inputs from each of these three divisions (G. associated finance management and commercial operation were centralized and coordinated through 2
.1. The short-term operation schedules were drawn up based on the coordination between these entities while the medium-term operation schedules were further coordinated with the short-term operation. and short-term operations. The medium-term planning activities include studies that are needed to be undertaken in timeframes of 1 to 5 years. In the literature. all activities of planning. erection and commissioning.to decide which generators would be scheduled for maintenance and when. T and D) and the CLDC. etc. Thus.

but usually undertaken individually or by an external entity. One important question that arises in these discussions is. independent of each other.
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. Policies. procedure and systematic organizational behavior pattern at all levels does not exist.1. Planning is no longer a centralized activity of the system. the utility had the overall responsibility of system operations and planning while in the context of deregulation.who is responsible to carry out the planning activities? In the vertically integrated structure. 4. each category of players have diverse responsibilities and interests.
Figure 1.in Deregulation (left) and in Vertically Integrated Environment (right)
The deregulated power industry structure (Fig.1. 3. Increased linkages because of horizontal expansion of number of participants in a category.information linkages between each and every division or sector. This makes the problems more challenging and involved. and similarly existence of multiple transcos and discos. The changes observed in the new power industry structure as compared to the vertically integrated system can be summarized as follows: 1. with the knowledge sharing of the system. 2.1 Comparative Linkage Diagram of Utility Operations and Planning. Missing / broken links between players because of allowed flexibilities in electricity market. figure on the left) led to deletion of the outer circle. split up of the G division to introduce multiple gencos in the system.

The operations coordination mainly involved determining the optimal set of solutions that minimized a system-wide cost function subject to a set of constraints.1. vertically integrated power system. such loss minimizing OPFs and centralized capacitor placement plans does not hold.1 Medium-Term Operations In the context of the classical. etc.1. 5-7]. The problem thus becomes far more complex in the deregulated environment compared to that in the erstwhile vertically integrated systems. reactive power planning typically involved a centralized optimal power flow (OPF) analysis for minimizing the system losses and hence determined the optimal capacitor placements in the system. In the competitive market environment. In such a context. 1. The local distribution companies (discos) are entrusted with the responsibilities of meeting the reactive power demand within their system while regional networks have their own areas of responsibilities. the overall planning for reactive power and voltage support has taken an entirely new meaning. medium-term operations have undergone a paradigm shift because of the diversification of functions and responsibilities amongst different entities in the deregulated industry structure. size of the system. The proposed and planned shut-down of coal-fired plants in 4
. and the problem now is a multi-level. in vertically integrated systems. For example. these self-generated schedules need to be coordinated with other gencos and subsequently with the independent system operator’s (ISO) reliability requirements.
1. when the ISO does not have jurisdiction over the whole network. multi-objective.2 The Ontario Power System and Its Electricity Market
In 1995.2 Medium-Term Planning The medium-term planning functions have also undergone changes in the way the objectives are formulated and issues are addressed. In 2002 the electricity market in Ontario became operational. However. availability of information and solution tools. Depending on the type of the system (hydrothermal mix. and its other system related constraints.1. hierarchical optimization and coordination problem.). a large number of methods were proposed to handle different technical issues in the medium-term operational time-frame. For example. In the context of deregulation. the medium-term operations planning problem can be addressed adequately [1. maintenance scheduling functions are now decentralized and gencos formulate their own maintenance schedules. the Ontario government initiated the process of restructuring of the province’s power sector in line with the Alberta electricity market in Canada and some US states.

Ottawa. The pricing of electricity and operating reserves in the Ontario electricity market is based on uniform price auction [9]. Minnesota. Brighton Beach with 580 MW and Transalta Energy Corporation with 510 MWs.170 MW. ESSA. East. North-East of Sudbury.720 MW. SouthWest /Bruce-GTA. Ontario has approximately 300 transmission sub-stations (up to 115 kV) and 30. Eastern Ontario-GTA. 220 kV and 115 kV lines. Niagara. Algoma-Sudbury. for operational matters the Ontario power system is divided into 10 different zones while as per the Integrated Power System Plan (IPSP) [8]. Barrie-GTA. Bulk transmission lines are classified into 500 kV.the province by the year 2020.2. It has a total of 27 inter-connecting tie-lines. Michigan and New York. OPA’s Planned Zones North-West. Within GTA. The market participants can also participate in physical bilateral contracts whose financial settlements can be done either through the Independent Electricity System Operator (IESO) or on their own. on the basis of their respective operating voltage levels. Bruce.
Ontario is interconnected with the power systems of Manitoba. West. Quebec.724 MW of capacity. operating reserves and Financial Transmission Rights (FTR) market.000 km of transmission lines. Brookfield Power with 1. the zones are re-defined as given in Table-1. except for a few sub-systems operated and maintained by other companies like Brookfield Power.840 MW from a total of 97 plants. There are few facilities operating at 345 kV in Ontario. Other major contributors are Bruce Power with a total capacity of 4. Majority of the transmission network is owned by Hydro One Inc. South-West. The Ontario’s electricity market is a real-time physical energy. Of these. Sudbury-Barrie. Currently. The IESO also procures ancillary services to ascertain the system security and reliability through a physical market for operating reserves and through contracts with licensed reactive support providers. Clearly OPG is the major player in the Ontario electricity market. because of environmental factors and the ongoing reduction in nuclear capacity due to nearing their life expectancy. Table 1. Ontario has 22 power generating companies having a gross generating capacity of 31. North-East. The Hourly Ontario Energy Price (HOEP) is the wholesale market price 5
.2 Zones of Ontario Power System Currently Defined Zones North-West. Greater Toronto Area. Ontario Power Generation (OPG) owns 41 generating stations contributing 22. has posed serious challenges for the electricity sector in Ontario [8].

the concept of short-term “centralized” dispatch (in the day-ahead / hour-ahead stage) has been transformed to market-auction based dispatch organized by the ISO / market operator. discos. have undergone or are currently undergoing a phase of restructuring and with that several associate issues have emerged because of governmental energy policies with regard to emissions reduction. Such medium-term operations may take into consideration fuel supply linkages and constraints. intermittent and transitional scheduling generators.) operating their individual businesses with conflicting objectives. The twelve interval prices thus obtained over an hour are averaged to obtain the HOEP. importance of renewable energy resources. as the case may be. This is particularly important because of the present day market price volatilities. retailers. including those in the developing countries such as in India and China. Medium-term operations studies in the electricity sector therefore have a major role to play in order that the whole system is operated in a secure and reliable manner in spite of various participating entities (gencos. reservoir draw-down scheduling in the medium-term and demand-side management options. The HOEP is charged to nondispatchable loads and paid to self-scheduling.
1. etc. oil price volatilities. and with increased reluctance of investors to venture into risky capacity addition projects. are briefly discussed below: Medium-Term Production Scheduling and Operations With deregulation. While the gencos typically seek to maximize their profit and accordingly carry out their production
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. The complexity arises in the coordination process because of the conflicting interests of the gencos and the ISO. etc. The market clearing price in Ontario is determined at every 5 minute interval. Medium-term production scheduling still has an important role and gencos need to carry out such scheduling which needs to be coordinated with other gencos by the ISO so as to ensure secure and reliable operation of the whole system. transcos.that varies throughout the day. There is also a need for undertaking medium-term planning studies that look at the system investment requirements from a closer time-perspective than the traditional long-range planning. ISO. based on prevalent supply and demand of electrical energy. Some of the specific issues that are of importance and relevance in the context of this thesis. finance and risk issues in new projects.3 Research Motivation and Objectives
The power sector in Ontario as well as in other parts of the world.

This important task used to be undertaken in a centralized manner in the pre-deregulation era. Even if they do develop such maintenance schedules. or reducing electricity 7
. In restructured power systems. the electricity customers would. In most of the electricity markets in North America. The ISO has thus. The resulting medium-term production schedules need to adhere to existing transmission and other system constraints. However. Locational Reliability Analysis and its Need It has often been argued that power sector deregulation has adversely affected the reliability and security margins in power systems [10]. while introducing market inefficiencies. it is also true that deregulation has brought about increased interest of power engineers to reliability issues because it provides a larger choice to the customers. upgrading transmission. each genco seeks to maximize its profit and in order to do so. be in a position to influence the price and reliability of the electricity service they receive. These locational prices provide important signals pertaining to the need of investing in new generation. and formulating a system-wide maintenance plan in the medium-term that results in a secure and reliable state of operation for the system. can often compromise the system security and reliability aspects by not developing appropriate maintenance schedules. In the current deregulated environment. the challenging task of coordinating all independent maintenance schedules from gencos. in the future. these schedules may result in an overall insecure state of operation of the system and hence are not acceptable to the ISO. is of paramount importance. ill-planned maintenance schedules can lead to unexpected rise in prices and may also impinge on the market operation. but needs a re-look in the new environment. leading to a trade-off between reliability and prices. Therefore a proper maintenance schedule developed by coordinating with all the market participants and considering the economic and technical aspects. these will be in their interests and may not be in the best interest of the system as a whole. It can be expected that as in other commodity markets. considering transmission constraints [11]. both at the individual genco level and at the systems level. Coordinated Maintenance Scheduling Maintenance scheduling is closely inter-linked to medium-term production scheduling and operations. the electricity prices are in terms of the locational marginal price (LMP) which reflects the cost of supplying the next MWh of electricity at a bus.scheduling.

However. whereas the increase in transmission capacity has been around 15% only [12].consumption. etc. it would also be pertinent if the ISO is equipped with a Load Service Probability (LSP) index that provides critical information on the probability of supplying load to the customers at a bus. It is therefore necessary to determine the level of LSP received by a customer. Reinforcement of Transmission System In most electric utilities around the world. recently some coal-fired units in Ontario have been shut down and some others (at Thunder Bay and Atikokan. the increase in power transfer capacity of the transmission system has been lagging the increase in generation system capacity. in order to ensure fair pricing. transmission system expansion has not received the attention that it requires and has not kept track with generation system expansion. This issue that has not been adequately addressed post-deregulation. For example. are essential elements in a well-functioning market to alleviate constraints. uncontrolled and unplanned power flow patterns. and needs to be examined because of the pressing requirements of system demand growth. There can be additional system specific issues that require strengthening of specific transmission corridors. in real life. Furthermore. penetration of distributed generation sources in the system. while feasible alternatives are being worked out. a premium on high LSP loads or a discount on low LSP loads can be introduced within the locational pricing framework. This is justified because each electricity customer in the power system attaches a different “worth” to its electricity usage and supply continuity. as per the IPSP. such a locational index can be integrated with the LMPs to arrive at a LSP differentiated nodal price for the power system and to charge the customers accordingly. in Ontario) are to be phased out (about 300 MW of capacity) within the next few years. The reduction in supply capacity can be met by importing power from other zones within Ontario but the transmission line capacities need to be reinforced. increase competition and improve the systems’ ability to meet the power demand. Such information on LSP will be very valuable to the ISO in order to improve its readiness for tackling system emergencies and other operational aspects. For example. propositions for such new corridors are extremely 8
. In the same way as the LMP provides vital information on system conditions to the ISO.and therefore. The annual load growth in North America is approximately 2% per year and generation capacity has seen a rise of about 30% in last three decades. The traditional transmission expansion planning problems involve developing new transmission corridors for power transfer. In other words.

The comprehensive framework will consider the individual gencos’ objective of profit maximization as well as the ISO’s objective of cost minimization. This is a fairly complex problem and requires the formulation of the problem as a twotier model and the synthesis of an update signal that modifies Gencos’ optimization constraint after the first-tier model (those of gencos) are executed. etc. To propose the concept of locational reliability. develop a methodology to determine novel locational reliability indices in power systems and further propose the application of this conceptual locational reliability to electricity pricing in deregulation. Such reluctance is due to possibility of environmental degradation from forest clearances for right-of-way. 3. which is then optimized to select one of the reinforcement options for each lines identified to be reinforced. transmission reinforcement is the most practical approach to cope effectively with demand-supply balance and transmission overloading issues. To address these issues in the medium-term. The coordinated framework does not require the ISO to develop maintenance schedules by itself. To develop a medium-term production-cum-maintenance scheduling framework applicable to participants in the deregulated electricity market environment. arising as a result of lack of adequate transmission capacity. but instead only requires it to verify the suitability of the individual genco’s maintenance plans from the perspective of overall system demand-supply balance. The 9
. ill-effects of electromagnetic induction on general public health. 1.4 Outline of the Thesis
The thesis is structured as follows.Chapter 2 presents a review of the theoretical background and the state-of-art in research on operations and planning activities in the medium-term framework.difficult to implement because of the reluctance of governmental agencies to approve them. Propose two different solution approaches and demonstrate the results on CIGRE 32 bus test system. 4. land contamination. To develop a novel scheme for the coordination of the production-cum-maintenance schedules of individual gencos with the system-wide security requirement of the ISO. This scheme will be based on the contribution of gencos to unserved energy.
1. 2. system reliability and security.1 Main Objectives of this Research 1.3. To develop transmission reinforcement planning (TRP) model that incorporates the engineering judgment and experience to determine a Feasibility Set.

presents the Ontario based example and detailed results of the coordinated maintenance scheduling problem. Chapter-7. Chapter-4. Chapter-5 discusses the novel location reliability indices.
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. the reliability-differentiated pricing concept. and presents the detailed results on a 5 bus-test system and the representative Ontario test system. In Chapter-6 the TRP problem is presented in detail and two approaches to its solution are suggested – the Decomposition Approach and the Unified Approach. The last chapter. summarizes the contributions of the thesis and discusses the scope for future research.detailed mathematical modeling framework of the proposed security coordinated maintenance scheduling problem is described in Chapter-3.

transmission loadings and wheeling penalties. uncertain and volatile market prices. All these activities being inter-dependent. it was essential to take up these inter-dependent activities simultaneously while carrying out operational planning exercise for a utility. not all the loss state would be affected. the power sector is faced with problems of demand growth far exceeding the capacity additions. the ISO needs to get involved in the coordination task so that the production schedules obtained by individual gencos are realistic and feasible from the systems perspective. and narrow operating margins. and several others. and highlights the need for optimal sharing of central sector generation. required coordination in order to achieve optimal operations since their isolated planning could lead to sub-optimal outcomes. then due to transmission limitation. The work also proposes a pricing scheme for inter-utility transfers. So LOLP is not an accurate indicator of the time for which unit i will reduce loss of load. Moreover. In the recent years after deregulation of the industry. Assuming that unit i-1 have been processed. Li and Singh [15] present a multi-area production scheduling model with a new approach to marginal cost calculation using the concept of probability of need of a unit i. Therefore. Parikh and Chattopadhyay [5] discuss medium-term operational issues pertaining to the Indian power system. Rau [14] has developed a Monte-Carlo simulation model for an interconnected power system that considers random outage of plants. Consequently.1 The Production Scheduling Problem in Medium-Term Operations
Production scheduling of a power utility in the erstwhile vertically integrated environment. A multi-area linear programming model is developed to quantify the merits of the integrated national grid operation in terms of cost savings.Chapter 2 Background and Literature Review
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. involved many activities such as generation scheduling. devising appropriate tariff for such transfers. if unit i is added. the concept of centralized production scheduling no longer holds true because of the individual operating strategies adopted by gencos. power flow computations. coordination of inter-utility transfers. fuel production and transportation scheduling. and identifies four inter-utility transmission reinforcement projects. One of the early approaches in medium-term power system operations studies consider a multi-period linear programming model to evaluate benefits from inter-utility transfers and trading between some US and Canadian states [13].

transmission constraints. which are of significance in the context of deregulation.So a new index of probability of need of a unit is proposed to improve the segmented global simultaneous decomposition approach for calculating production cost.2 The Maintenance Scheduling Problem in Medium-Term Operations
Maintenance scheduling of generating units is an important medium-term operations activity that reduces the risk of capacity outages. for example load demand profile and seasonal variation 12
. Traditionally such coordination is developed by the ISO trying to minimize the total cost of the system. The sale transactions between two utilities is a complex decision as it is coupled with the system demand and reserve. Electricity sale transactions are integrated with the medium-term scheduling problem using a mixed integer programming (MIP) model in [16]. the issue of coordination between medium-term generation planning and short-term planning activities has been examined. and the decisions have to be made in conjunction with commitment and dispatch of units. The report identifies emission constraints. network decisions such as capacitor placements while incorporating the maintenance decision impact are discussed.
2. improves unit availability and hence system reliability. Results are obtained for a Norwegian power producer participating in NordPool. for example the issue of optimal utilization of limited energy resources. Various factors can affect the system maintenance schedules. and a post-analysis (as a feedback loop) as the major issues in operations planning. In a recent work [18]. In the same context [4] discusses the need of coordination between different decisions in a same time-frame. An integrated maintenance schedule for the bulk power system is usually developed and such coordinated plans can improve system operational efficiencies significantly. The work maximizes the expected revenue of a genco from its energy generation and forward contracts in the market. Another recent work [19] addresses the optimal management of hydro resources in the mediumterm. the Nordic power exchange. impact of uncertainties. Coordination between different decision levels is important in order to guarantee that certain aspects of operation that arise in the medium-term are explicitly taken into consideration. The importance of integrated models for analyzing fuel-supply decisions at the generator level. having an appropriate maintenance schedule is very important but frequent and unnecessary maintenances can drastically increase operating costs and reduce supply continuity and unit availability. The 1992-IEEE System Operations Sub-committee [17] report some major issues in operations planning. Therefore.

Strategically. the ISO usually does formulate a maintenance schedule annually for all generators in the system by maximizing the social welfare. can be listed as follows1) Levelizing the reserve [1] 2) Levelizing the risk or the Loss of Load Probability (LOLP) [24] 3) Minimizing the annual LOLP [25] 4) Minimizing the total maintenance cost [26] In competitive electricity markets. In spite of such different objectives of the involved players. In the context of vertically integrated operation. and so on till the next cycle. As reported in [20. 2-weeks. requiring say. the ISO can negotiate an appropriate maintenance schedule with the
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. the elapsed time from last maintenance.of the system demand need to be considered when devising the schedules. 27-29]. ensuring system reliability is the primary responsibility of the ISO while the gencos’ primary objective in its production-cum-maintenance scheduling tasks is to maximize its profits. However. the amount of maintenance required on a specific unit. This can be modeled by a variable elapsed time instead of having a fixed elapsed time. while year after still more. Planned outages of power plants have a cyclical pattern. The next year's maintenance would be simple. Condition based maintenance scheduling can save on cost of maintenance as well as increase unit availability and revenue collection without affecting the reliability. and such other factors are critical. A major maintenance may be conducted every 5-6 years and take 5-10 weeks for a complete overhaul. hydro energy availability and the extent of hydro-thermal mix in the system. The maintenance decisions for a unit can also be deferred by a year or so. Some researchers have also argued in favor of monitoring the condition of generating units and hence decide the maintenance requirement upon verifying the results [20-23]. Similarly. for the ISO and the gencos are quite different. maintenance intervals and durations. the unit sizes. but cannot impose it on the participating gencos because these gencos seek to maximize their profits by scheduling units on maintenance such that their respective loss of revenue due to maintenance outages is the least. Some of the well known objective functions for maintenance scheduling problems used by researchers. 21]. The optimization problems therefore. in principle. the ISO would like to schedule the maintenance during low demand periods while the gencos would choose to schedule their units on maintenance during low price periods. lot of research has been reported on the development of efficient solutions to the maintenance scheduling problem or to address new issues within the scope of this problem [1. this aspect has not been examined or addressed in this thesis.

A composite system maintenance coordination problem in deregulated environment is presented in [29] wherein the method of coordination between gencos. Shahidehpour et al. Conejo et al. [21. and inter-utility transfer schedules. the well-known levelized reserve method [1] seeks to equalize the reserve for each month of a year. while transmission constraints are incorporated using a dc-OPF formulation in [34]. In [21]. 35-37] propose the use of decomposition techniques to coordinate the optimization of various objectives among the self-optimizing entities of the market. The levelized risk method [24] attempts to achieve a uniform LOLP for all months in a year. Among various methods proposed to address the maintenance scheduling problem. A traditional technique is to schedule the maintenance to levelize the load plus capacity on outage over a year. in a manner acceptable 14
. resulting in a minimum annual LOLP maintenance schedule. Though this method is widely used because of its simplicity. A two-level hierarchical method for levelize incremental risk is proposed in [25]. the maintenance scheduling of a power plant using the reliability criteria of maximizing ‘minimum reserve’ was proposed. wherein a MIP model is developed taking into account fuel supply and transportation decisions. Decomposition techniques are of significance because of their ability of solving very large-scale problems. In most systems. Chattopadhyay [32] proposed a practical method for maintenance scheduling using linear programming. The paper discusses the effects of cost. the problem of maintenance scheduling in restructured power systems is described and the use of decomposition techniques to coordinate the optimization of various objectives among the independently operated entities is discussed. In a subsequent work. the regulatory agreements require the gencos to schedule their mandatory maintenance by negotiation with the ISO. the transco and the ISO is based on the practices adopted by ISO. reliability and constraints on each other when addressing a maintenance scheduling problem. Inter-area transfers and stochastic reliability constraints are included in [33] for maintenance scheduling and the problem is solved using Bender’s decomposition method. An integrated approach to least-cost maintenance scheduling of generating units for interconnected power systems is presented in [26].gencos in order to guarantee an adequate level of security of the system. production and maintenance scheduling decisions. it does not incorporate random outages of generating units. It considerably improves the convergence and reduces the computational burden over integer programming methods. In [31]. [28] presents a coordinated maintenance scheduling approach in restructured power systems that uses an iterative procedure of coordinating the schedules between the ISO and the gencos such that an appropriate degree of reliability is attained over the year. In the context of deregulation. The method is extended in [30] to include network constraints.

obtained with the objective of maximizing profit to ISO. An incentive is proposed for generators willing to alter their maintenance schedules for the sake of reliability while penalizing those not altering. A common-mode or cause model is applied in composite system reliability evaluation. customers and all involved parties would indeed welcome such information if made available in advance.to all. stability and reliability limits.
2. does not specify the bus where the unserved load is expected. It is to be noted that the LOLP. however. [38] takes into account the forced (and planned) outage rates of generating units and provides a quantitative measure of the expected duration. Transmission congestion can force the system to operate at a sub-optimal dispatch point resulting in a low value of LSP. which is compared with an ISO-generated schedule that is obtained by maximizing a reliability index. that the system is not able to serve the load. On the other hand. Transmission constraints are incorporated using a linear flow model. in a given period. The LOLP index furthermore.3 Locational Reliability and Reliability Differentiated Pricing
One of the commonly used reliability indices. For example..e. The long-term scheduling of transmission is useful in determining the available transfer capacity in the system. does not provide enough information when transmission congestion is present.16 minutes (i. In [37] an integrated generation and transmission maintenance scheduling is presented which uses Benders decomposition approach to solve the optimization problem. Shahidehpour and Marwali [36] presented a long-term transmission and generation maintenance scheduling problem in the context of deregulation. A two-stage scheme is developed where the gencos submit their maintenance schedules. Reliability evaluation of a composite system involves the simulation and load flow analysis of each state of the system over a desired period [39]. the LOLP [1]. it can be appreciated that the ISOs. 24 hours x 60 minutes x 0. In [34] the network constraints are refined by using a dc load flow representation while determining the maintenance schedules. This is very important in the context of power system operation in deregulated environment when systems are operating at close to their security. A distinct set of measurable reliability indices are defined in 15
.0015) over a given day. incentive and disincentives are determined and modified schedules for generators are determined until a feasible solution is achieved. Location specific information on LSP can assist the ISOs to improve their readiness for an event. If the submitted plan fails to meet the reliability criteria of the ISO. a day’s LOLP of 0.0015 implies that the system load will remain unserved for the duration of 2.

a technique for reliability evaluation is proposed wherein a complex radial distribution system is reduced to a series of general feeders using reliability network equivalents.[40] with reference to load buses in a practical system. then failure at any load bus due to component failure is conditional upon the load exceeding the defined carrying capability of the remaining facilities.4 Transmission Reinforcement in Medium-Term Planning
The objective of transmission expansion planning is to determine the installation plans of new facilities so as to enable the resulting bulk power system to meet the future demand at least cost. At times of shortage of supply or outages. Wang et. political and financial constraints [47]. Interruption Duration. Load Interrupted. The requirements are contradictory as higher reliability means higher investment cost 16
. a new technique to determine nodal prices and nodal reliability indices based on probabilistic evaluation approach considering customer outage costs. Unsupplied Energy and Interruption Severity. Guidelines for measuring the load bus reliability is presented in [41] via a useful set of terms and procedures for consistent reporting of bulk power system reliability. while satisfactorily meeting the prescribed technical. A reliability differentiated pricing of electricity considering outage cost and priority pricing (for customers who desire supply continuity) is proposed in the context of vertically integrated power systems in [45]. It is demonstrated that these indices have unique characteristics because of differences in system topology and operating conditions. The aim of transmission planning is therefore. A conditional probability approach is used in [44] to determine the reliability at any point in the composite system. Researchers have examined and proposed reliability indices at a bus in a composite power system. The concept of delivery point reliability index probability distributions has been recently proposed in [43] which are obtained using a sequential Monte Carlo simulation approach. al. environmental.
2. The failure at a load bus is defined as a loss of load or a resultant voltage limit violation at the bus [38]. Basic equations are used to calculate the individual load-point indices. differentiated prices for the various customer classes is proposed based on their respective outage costs. In [42]. These are. legal. Interruption Frequency. The work argues that if the load can be considered a random variable and described by a probability distribution. considering generation and transmission. presented in [46]. instead of having one market clearing price for all customer classes. to establish where and when to build new transmission lines with associated equipment required for economic and reliable supply of forecasted load. Average Duration per Interruption.

can be opted for.and hence the planner has to make a compromise such that adequate reliability is achieved at an affordable cost. new generating sites (as per generation expansion plans). 50]. Transmission expansion planning problems. duplexing. Various line capacity reinforcement options can be exercised on an overloaded line. some of the reinforcement options such as. over and above the cost escalation factors. 49. or as a static transmission expansion problem. reconductoring. voltage levels. to increase its power handling capacity. have been used since the sixties. non-linear network performance indices. cost of unserved energy. Alternate heuristic approaches have been proposed to address the problems of realistic systems. Expansion studies have tried to transform the multi-year. The system overload is alleviated by increasing the power handling capacity of existing bottlenecked transmission lines without altering the right-of ways. The investment decisions depend on the configuration of transmission lines required and the voltage level at which additions are needed. integer programming methods. right-of-way availability. long term planning problem into a yearly optimization problem. ignoring the time-dependence of planning proposals. and the transmission reinforcement planning (TRP) problem which typically span up to 5 years. have largely being studied either as a single stage. Optimal planning of an electric transmission network requires the determination of the most economical expansion plan over a specified period. The system expansion should take into account load growth. In this
17
. Transmission expansion planning has received considerable attention amongst researchers over the years. To address these issues in the medium-term. A typical cost function includes both fixed and variable costs of all new line additions. arising as a result of lack of adequate transmission capacity. with research spanning over diverse issues and solution techniques. adding new circuits or even voltage upgrading of lines. reliability and social cost. one stage synthesis. series compensation. Depending on the type and the amount of transmission line overloading [48. transmission reinforcement is the most practical approach to cope effectively with demand-supply balance and transmission overloading issues.. driven by their size. considering a cost minimization objective subject to a set of linear constraints. With regard to methods of solving the problem. This has been further generalized to include cost of power losses. The problem of transmission expansion planning can be categorized either as a long-term planning problem in which the decision making exercise spans over a horizon of 20-25 years or even more. Recently artificial intelligence (AI) and hybrid-AI based methods have been used to address transmission expansion problems. system interconnections etc.

al. the TRP problem has been considered in order to align it in the same time-frame as with the other issues that have been addressed in the different chapters of this thesis. Villasana et. siting of new generation and new voltage levels. by making use of guide numbers and overloads. it solves a relaxed problem. Garver [47] identifies new circuit additions to relieve capacity shortages. [51] suggested a long-term transmission planning procedure. The solution arrives at an optimal plan.. Lee [52] uses a branch-and-bound integer programming technique to solve a single-stage transmission expansion planning problem. Thus the model provides an orderly means of examining the effect of addition of new lines to transmission network and selecting lines that makes greater contribution to system’s economy. reliability analysis and economic evaluation. 18
. Minimization of losses results in a flow estimate that indicates the links on which a circuit should be constructed so as to minimize the new circuit mileage. The linear flow estimation method replaces the electrical network problem with linear programming problem.. Romero and Monticelli [55] propose a hierarchical decomposition approach for optimal transmission network expansion planning. which combines the otherwise separate computations of load flow. Initially.thesis. the relaxed constraints are then reintroduced as the final solution is approached. prior to evaluating the economic investment decisions. the operation cost and the reliability cost.. A linear model is developed that determines the line capacity additions required to meet the power injections. al. The method reduces the computational burden by using a dc-load flow model. These are then checked for compliance with system reliability constraints. etc.[54] addresses long-term issues such as new load growth. Serna [53] treats the transmission system as a transportation network and proposes a method comprising a simulation process for the calculation of the loss of load and a heuristic optimization process to select the reinforcement to the network. Kaltenbach et. The network estimation procedure is carried out in two stages of linear flow estimation and new circuit selection. The hierarchical approach solves the planning problem in three stages. using linear programming. Load flow estimation is subsequently carried out to ascertain the network capabilities for handling the power flows. Arriaga and Bayona [56] formulates the long-term expansion planning problem as a static optimization problem of minimizing the global annual cost of electricity production. by combining linear power flow and the transportation model. which is obtained as a sum of the annualized network investment cost. by taking advantage of natural decomposition between the investment and operation sub-modules.

The IPSP outlines that the transmission system needs to be strengthened in order to1) achieve the long-term supply mix targets 2) facilitate development of renewable energy sources [59] 3) facilitate phasing out of coal-based power plants (once system adequacy and reliability issues are taken care of) to address environmental concerns
19
.. Gajbhiye et.) and the IESO. This plan document describes the areas for investment needs and available options for possible reinforcement and expansion of the transmission system. In the medium-term context. Three sets of rules are defined viz. The reactive power planning problem can also be seen as a part of the TRP problem in the medium-term. the Ontario Power Authority (OPA) has presented the Integrated Power System Plan (IPSP) [8] in consultation with participating members of the Ontario electricity market (genco. In the context of Ontario. the transmission expansion planning problem is typically transformed to the TRP problem where the existing system configuration is considered and the most suitable options for strengthening the bulk transmission system are examined. Ampacity and. discos. [48] propose an expert system approach to short-term transmission expansion planning. with the cost of new corridor additions. Reactive Power Management rules. 58]. Transmission reinforcement problems have been addressed in the context of vertically integrated systems in combination with medium-term operations scheduling in [5. The reinforcement of new lines are decided based on the duals of the transmission line constraints in [5] while the addition of new circuits is decided by implementing a mixed-integer optimization problem in [58]. The reactive power management issues are also addressed for voltage control. to develop an expert system approach for multi-year transmission expansion planning. etc. al. considering both thermal and MW capacity increments. the need for network expansion is determined and a compromise between congestion cost and expansion cost is used to determine the optimal scheme for expansion. Baldick and O’Neil [49] estimates the costs of strengthening system load supply capability through transmission reinforcement technologies without altering the right-of-ways. Very recently. transco. MW control. A rule-based network augmentation is carried out to reduce investment cost and alleviate the network congestion. They compare the cost of transmission reinforcements. Shrestha and Fonseka [57] use system congestion as a driving force for transmission planning.In the context of deregulation. Based on the level of system congestion.

the need for a locational reliability index is brought out. locational reliability and the TRP problems in order to develop an understanding of the issues and the state-of-art in the research in these pertinent subjects of medium-term operations and planning in power systems. Subsequently. reduce transmission congestion and facilitate the integration of new generation in a cost effective way. A modest attempt is made in this chapter to review the literature on production-cum-maintenance scheduling. the medium-term planning issues are discussed with particular emphasis on transmission reinforcement which has not received adequate attention so far. maintaining system reliability
2.5 Concluding Remarks
This chapter discusses the pertinent medium-term operations issues of production and maintenance scheduling in power systems and brings out the changed paradigms of operation and the need for coordination of these functions by the ISO in the context of deregulation.4) increase the system operating efficiency. Thereafter.
20
. which can provide the ISO with critical information pertaining to the probability of serving the customer loads.

pp. Bhattacharya. they would seek to maximize their medium-term profit from an optimal production-cum-maintenance scheduling program. The proposed framework uses the concept of domains and commons [60. Barot and K. Nov. hydro energy availabilities and other related constraints. See Appendix D for the IEEE Copyright Form. The ISO also takes into account the system demand balance over the medium-term. It is to be noted that in this proposed framework. 61] to allocate the unserved energy at a bus. No. and these are allocated to a set of generators (and hence gencos) responsible for such unserved energy at various buses during a particular period over a year. and hence directing them to alter their maintenance schedules in specific periods and re-submit. 23. It can be realistically assumed that since the genco are operating in deregulated electricity markets. These maintenance schedules are submitted to the ISO.1 Introduction
This chapter presents a new approach to coordinated maintenance scheduling in the deregulated electricity market environment.Chapter 3 Security Coordinated Maintenance Scheduling in Deregulation Based on Genco Contribution to Unserved Energy: Mathematical Model 1
3. using information on bus-wise unserved energy. in its analysis of the system operation incorporating maintenance schedules. Security coordinated maintenance scheduling in deregulation based on genco contribution to unserved energy. In this method the gencos submit their respective maintenance schedules to the ISO. 1871-1882. transmission line capacities. Vol. IEEE Transactions of Power Systems. 4. which is responsible to ensure that the system security is maintained while taking into account the scheduled outages of generators provided by individual gencos’ maintenance schedules.
1
21
. but instead it generates corrective signals for each individual genco. 2008. The iterations
Some parts of this chapter has been published inH. The maintenance scheduling approach described here can ideally be termed as a levelized reserve with network constraints type of approach. This unserved energy arises when gencos’ maintenance schedules are considered. the ISO does not generate a maintenance schedule by itself.

using information on bus-wise unserved energy. A novel contribution factor is then introduced to allocate the unserved energy. The ISO executes the OCP program (discussed in Section-3.3. o The UPDATE algorithm uses the concept of domains and commons [60] to determine the generating units (and hence gencos) accountable for the unserved energy at a bus. It considers the system demand-supply balance. Section-3. and there is no unserved energy at any bus. yield a feasible medium-term security constrained production and operations schedule for the system as a whole. o The OCP calls an UPDATE algorithm (Section-3. It can be realistically assumed that the gencos. 22
. in the system. o The iterations between the gencos and the ISO takes place until the coordination program has converged.1) and the maintenance schedules are submitted to the ISO. or for any period. in its medium-term operations coordination program (called the OCP.1). The individual gencos will execute their respective GMS programs (discussed in Section-3. o The ISO is responsible for ensuring system security and reliability while taking into account individual gencos’ maintenance schedules. Section3.4. The basic functioning of the proposed procedure is as follows: o First.between the gencos and the ISO takes place until the coordination program has converged. at certain buses and periods when considering the genco’s maintenance schedules.2) to ensure that the submitted schedules from all gencos. when put together.
3. or for any period.2) for verification of individual genco maintenance schedules. some unserved energy may arise.3. operating in deregulated electricity markets. In the present work. to the gencos accountable for it. in the system. At this stage. and there is no unserved energy at any bus. hydro energy availabilities and other related constraints.2 Overview of the Proposed Coordination Scheme
Fig.2) which synthesizes corrective signals for specific defaulting gencos. transmission line capacities. seek to maximize their medium-term profit from a production-cum-maintenance scheduling program (called the GMS Program.3.3. the gencos submit their respective maintenance schedules to the ISO.3. and directing them to alter their maintenance schedules in specific periods. a new approach to security coordinated maintenance scheduling in deregulation is proposed.1 presents an overview of the proposed coordinated maintenance scheduling problem.

GENCO 1 MAINTENANCE SCHEDULING PROGRAM
GENCO 2 MAINTENANCE SCHEDULING PROGRAM
GENCO i MAINTENANCE SCHEDULING PROGRAM
ISO COORDINATION PROGRAM
FEASIBLE SOLUTION OBTAINED?
GENERATE CORRECTIVE SIGNALS USING UPDATE ALGORITHM
FINAL RESULTS
Figure 3. during a given period. The accountability of a genco to serve a specific load is computed using the novel generation contribution factor method and this information is used to trace back the source of the unserved energy at a bus and generate update signals for the defaulting gencos.If the gencos’ submitted maintenance schedules result in violation of system constraints. corrective signals are synthesized by the ISO and sent to those gencos which are accountable for the resultant unserved energy at various buses. because of their maintenance schedule. The gencos are directed to modify their maintenance schedules based on the corrective signals and re-submit to ISO. then.1 Flowchart Showing the Proposed Coordinated Maintenance Scheduling Approach
23
. This iterative scheme is continued until a feasible medium-term production schedule is achieved by the ISO.

t. In the first iteration."Base"
(3..t. namely. b k t b
− ∑ ∑ ∑ (Cc k Wk.1."Peak" ≤ S k.1.1). enforce the start-up logic for generating units. t.b + Cg k Pg k.. the model is solved without any intervention from the ISO.3. Three price intervals.3 Mathematical Model Formulation
3. 3.. 3.3 Start-up Logic Constraints These constraints. The second term denotes the genco’s medium-term production costs comprising generators’ no-load. imposing hard constraints on unit maintenance schedules.2) considers the change of status between the last sub-period of a period and the first sub-period of the following period while (3.1.t − 1.2) and (3.3. The third term represents the genco’s gross maintenance costs over the year. The medium-term market price is modeled using Price Duration Curves.b )Tt. Constraint (3.2 Constraints 3.3).b k t b Max − ∑ ∑ Cm k Pg k X k. (3.1 Genco Maintenance Scheduling (GMS) Program The GMS Program is a mixed-integer linear programming model.
Wk.
Ω U = ∑∑∑ρ Pg T t.2)
∀t = 2.t.3.t k t
[
]
(3. is the maximization of its mediumterm operating profit (3.1)
The first term of (3.3) takes care of the status change over two consecutive sub-periods of the same period. b t. b k. intermediate and base prices are assumed for each period (month) of the year. peak.b + Cs k S k.1) denotes the gross revenue earnings of the genco in the medium-term assuming that it sells all its energy to the market. variable and start-up costs. In subsequent iterations the GMS Program is solved taking into consideration the ISO’s corrective signals.12
24
.t."Base" − Wk.t.3.3.1 Objective Function A generic objective from the perspective of a specific genco U. if necessary.

12)
It should be pointed out that the GMS Program described by (3. [62]-[63]. Therefore. [26].∑ X k.3. In (3.12). t representing hydro energy availability of unit h at period t can be assumed to be
3.4. These maintenance scheduling models are fairly well established and accepted widely.t. if they have to receive a corrective signal from the ISO. avoiding detailed reservoir balance constraints [4]-[5].4.
Max ∑ Pg h. such as CPLEX.b Pg h E h.b Tt.9 Hydro Energy Constraints These constraints limit the energy scheduling from hydro generators depending on water availability in the reservoir over a given period of time.10 Maximum Allowable Capacity on Maintenance (Corrective Constraint) This is a conditional security constraint externally imposed by the ISO in the second and subsequent GMS Program iterations of some specific gencos u (u ∈U).10)
3.
(3.11)
The parameter Eh.t × Pg k u k
∀ t∈m
(3.
Max ≤ γ ∑ X k. It is a simpler representation that captures the energy allocation to hydro units at a specific period.2 and 3. They are linear mixed integer type optimization problems and can be solved using various available solvers.1. the main emphasis of this work is to develop the coordination mechanism between the gencos and the ISO after the individual maintenance schedules are obtained.12) γ is the corrective signal (in MW) to genco u (specifying the allowable maximum capacity on maintenance in a particular period).1.3. The constraint ensures that genco u modifies its maintenance schedule by limiting its total capacity on maintenance during the ISO-specified period m to a certain maximum value.3.12) is fairly similar to the genco-level maintenance scheduling model in [7] except for the conditional constraint (3.b ≤ ∑ Tt.
26
.t b b
known to the ISO in the medium-term framework. The details of synthesis and handling of this corrective signal is discussed in Sections-3. [32].1)–(3.t ≤ NM t k
(3.

b ⎣ ⎦
3.3.b ⎤⎥Tt.3.i.
Cost = ∑ ∑ ∑ ∑ Pg K . b t b i K + ∑ ∑ ∑ En i .t. [63]-[64]. This is a linear (transportation model) representation of power flows.13)
3.3 Supply-Demand Balance Constraint Constraint (3.i ≥ ∑ PDi.2 Operations Coordination Program (OCP) of the ISO The OCP executed by the ISO is very similar to the production scheduling models discussed in [4] and [5].b + RSVt . i Tt .2.t .i. b × Cn t . b t b i
3.b
⎦
⎢l j ⎣
⎥ ⎦
(3.j. t . t .2.3.13) and the cost of unserved energy (second term in 3.3.2.b ⎢ l j i. [26].j ) × Pj.b ⎥ t. with line losses modeled using a loss factor that is a function of line voltage class [4].b t.
Max ∑ ∑ 1 − X K .t Pg K .b 1 − Aux K ⎣K ⎡ ⎤
(
l l )⎤⎥Tt. [5].t.1 Objective Function The ISO’s objective function in the OCP is minimization of total system cost which includes total cost of generation (first term in 3. [56].b + ⎡⎢∑ ∑ ( 1 − LFi.b i K i
(
)
(3.15)
27
.
⎡ ⎢ ∑ Pg K.2 Constraints
(3.14)
l − ⎢∑ ∑ P = PDi. intermediate or base) is met by generation at the bus and power imported (net of exports).3. 3.13).t.3.t.bT ⎥T + En i.t.4 System Reserve Requirement This constraint ensures that the overall system has enough generating capacity in service at all times and some amount of reserve (as a fixed percent of demand) is available. i .14) ensures that the energy demand at a bus for given sub-periods (peak. It is assumed that the ISO would mandate that gencos submit their medium-term operating costs (Cg) along with their initial maintenance schedules.2. b Cg K .

j .3.2. i ⎝ ⎠ ⎞ Pg Min Pg K . b ≥ ⎛1 − X ⎜ K. i.b ⋅ E H. 3.4. b ≤ TLl .2 while the UPDATE algorithm for synthesizing the corrective signals is given in Fig.18)
3. t .3. i ⎝ ⎠
(3. j = 0 i
(3. These accountabilities are derived using the concept of commons and domains.i.4 Coordination Scheme Based on Gencos’ Contribution to Loads
The coordination scheme for the ISO is based on determining a gencos’ accountability to the unserved energy at a bus. i.3.2. t . The master program of the complete iterative scheme is given in Fig.19) (3.20)
3.16) (3. t . The complete iterative procedure of coordinated maintenance scheduling can essentially be divided into three modules and is described in the following sub-sections. is limited by hydro energy availability over a period t. j .
Pil.
Max ∑ Pg H.t. t ⎟ K.t b b
(3.3.17)
3.b ≤ ∑ Pg H ⋅Tt.3.6 Hydro Energy Constraint This constraint ensures that energy generated from a hydro unit H. given by (3. j × PlMax i
Pil. 3.7 Line Capacity Constraints The power flows on transmission lines are constrained by line capacities which depend on the transmission line voltage. that system security (line limits) is not violated and the system meets the demand at all times (no unserved energy at any bus). Subsequently corrective signals are derived for these gencos to modify their maintenance schedules. the ISO executes the OCP.2.b ⋅ Tt. b = 0 ∀ TLl . 3.13)-(3.5 Generation Capacity Constraints
⎞ Pg Max Pg K .1 Verification Process After the gencos submit their maintenance schedules to the ISO. by incorporating these decisions as inputs and verifies whether the medium-term operations schedule for the whole system is feasible.20). b ≤ ⎛1 − X ⎜ K.t ⎟ K.
28
. t .

the maximum unserved power (PnMaxm) and the corresponding period m (m ∈ t) are noted. From this. network congestion can also be attributed to the unserved power at a bus. if a group of generators (G) is responsible to serve a particular load at a bus i. there will be a proportionate unserved power at bus i. and the bus-wise distribution of PnMaxm. if G experiences a percentage capacity outage. then the same group G is responsible for not supplying the load at bus i. Therefore. We can also determine the set of buses N1 that contributes to PnMaxm in period m.
29
. when an unserved power is observed at the bus i. Under some circumstances. m. Further elaborating. It is obvious that the unserved power at a bus is either due to network constraints or shortage of generation capacity. it can be proportionately allocated to the responsible generators in G and hence the responsible gencos. denoted by Pni. the system may not be able to cater to the load in certain periods (or sub-periods) when large capacity generators are on maintenance simultaneously. The consequent buswise unserved energy is determined for every sub-period b of period t. According to the concept of domains and commons [60].When the ISO executes the OCP.

3.4.2 Synthesis of Corrective Signal- UPDATE Algorithm The generating units (and hence the gencos) responsible for the unserved power at various buses are determined using the UPDATE algorithm (Fig. 3.3), and the ISO synthesizes appropriate signals for them to update their maintenance schedules. The following steps are used: a. Call ALLOCATE algorithm (Section-3.4.2.1) Inputs: Set of buses N1 (N1 ∈ N) which have unserved power at period m; the unserved power Pni,m, (i ∈ N1); other outputs of OCP such as line power flows and production schedules. Outputs: Set of gencos u (u ∈ U) corresponding to each bus N1 responsible for Pni,m. b. Define Fractional Capacity on Maintenance (βu) for the set of gencos u, as follows:
βu = MCAPu TCAPu

(3.21)

βu represents the fractional capacity of a genco u on maintenance during period m.
c. Determine the proportionality constant αu (3.22) to allocate bus-wise unserved power to each genco u in proportion to its Fractional Capacity on Maintenance.
αu = βu ∑ βu u

(3.22)

d.

Use αu to allocate the bus-wise unserved power to genco u as follows:
Pni,m,u = αu ⋅ Pni,m

(3.23)

e.

Accumulate contributions of each genco u in total unserved power for the period m.
N1 Pnm,u = ∑ Pni,m,u i =1

(3.24)

f.

Calculate the maximum allowable capacity on maintenance (γu) for a genco during period m. This is the update signal synthesized by the ISO which will be sent to the set of gencos u (u ∈ U).
γ u = MCAPu − Pn m,u

(3.25)

32

3.4.2.1 ALLOCATE Algorithm- Generators Accountable for Unserved Energy The concept of domains and commons was proposed in [60] to determine the set of generators that supply a load at a particular bus. The ALLOCATE algorithm is developed based on the same concept, but to determine the set of generators that are accountable for unserved power at a bus. A generator k connected to the system and injecting power in the network contributes simultaneously to loads at several buses. A domain can be defined as that set of buses in the system which can be reached by k, and this set is known as the domain list of k denoted by DLk. Since the power demand at a bus may be catered by more than one generator, it can be expected that the domain list of one generator may contain buses that exist in the domain list of another. To obtain a unique set of buses without overlap, the notion of common is formulated using the domain lists of all k. A common can be defined as the set of buses that are supplied by the same group of generators. The common is designated by Cp,kL where p is the index of the common and kL represents a unique group of generators that supply member buses of common p. Fig. 3.4 and 3.5, presents the complete procedure for determining the domains of all generators in the system and then determining the commons. The steps followed to construct the domain list are: a. b. c. From the set of generator buses NG, the first available generator bus, corresponding to generators K, is placed in the ‘To Be Domain List’ of K (TBDLK). Transfer the first bus in TBDLK to the domain list (DLK). Examine branches connected to this bus i and the power flow directions in each branch. These power flows are obtained from the OCP, for the period with maximum peak load, and all generators online. d. e. f. If the power is flowing out of a branch at bus i, then the opposite end bus is added to TBDLK. If any bus exists in TBDLK and is not part of DLK, then repeat from Step-b. If no buses are left in TBDLK, then the domain list DLK is complete. If all NG are not considered, repeat from Step-a to determine DLK for all K. After the domain list DLK is obtained, for all K (∀ U), the steps to formulate the commons are as follows a. With DLK (∀ K) known, group the set of generators kL contributing to load at a bus i. Do this for all i (i ∈ N). 33

b. c. d.

For all N, take a bus i and if this bus is not a part of any common Cp, kL, then create a new common corresponding to kL supplying the load at i. Determine branches connecting to i and for every branch if the opposite-end bus is supplied by kL, then put the opposite-end bus in Cp,kL. Repeat from Step-b, until all buses are considered.

34

4 Flowchart of the ALLOCATE Algorithm (first section)
35
.Figure 3.

4. The process of modifying schedules.12) is applied to period m as a hard constraint for subsequent iterations.3 Handling of Corrective Signals by a Genco On receiving a corrective signal γu (a specified maximum allowable capacity on maintenance) from the ISO.5 Flowchart of the ALLOCATE Algorithm (second section)
3.12). verification and synthesis of corrective signals is repeated until a 36
. as the period with maximum unserved energy. The constraint (3.Figure 3. re-submitting. This ensures that period m does not default again. the particular genco-u incorporates it as a corrective constraint for period m (3.

6 Flowchart for Acceleration of the Convergence
37
.4 Accelerating the Convergence Process The proposed security coordinated maintenance scheduling scheme is an iterative process and fast convergence to a feasible solution is critical.6 that decides whether to constrain one or two periods simultaneously.4. The feasible solution is one when there is no unserved energy at any bus. etc. an approved final maintenance schedule for all gencos and other information on line power flows. corrective signals are synthesized and corrective constraints can be applied to the top two defaulting periods (m and m’) simultaneously if the unserved powers at these periods are close in magnitude in a given iteration. 3. On convergence.feasible solution is obtained. the final results are processed that contains a medium-term production schedule for all gencos and their generators. at any period. as shown in Fig. To accelerate the convergence process. bus marginal costs.3. A simple algorithm is used.
Figure 3.

The final solution so obtained. In the next chapter. Based on the calculation of gencos’ accountability to system unserved energy. The coordination is carried out by the ISO after individual gencos submit their preliminary maintenance schedules. is the set of genco schedules that maximize their respective profits while meeting system security constraints implemented via line flow limits for different voltage classes. a detailed case study has been presented by considering a representative Ontario power system data set to bring out the important aspects of the proposed scheme and to examine the performance of this coordination mechanism.
38
.5 Concluding Remarks
This chapter presents a new scheme for security coordinated maintenance-cum-production scheduling for multiple gencos operating in the deregulated market environment. the ISO computes and synthesizes corrective signals to defaulting gencos and these are incorporated by these gencos as hard constraints in their revised maintenance schedules. along with other system constraints.3. The medium-term production schedules that are also obtained from the same scheme can be used by the gencos as guidelines for their medium-term operations.

because of the difficulties associated in obtaining private cost information of generators from individual gencos. Security coordinated maintenance scheduling in deregulation based on genco contribution to unserved energy. with total generating capacities of 4270 MW and 5950 MW respectively. for the purpose of these studies. spread over 13 generating buses. IEEE Transactions of Power Systems. Bhattacharya. 39
1
. 4. See Appendix D for the IEEE Copyright Form. Genco-1 has a fully thermal-based portfolio while genco-2 is a wholly hydro-based utility.
Some parts of this chapter has been published inH.1 Gencos’ Profiles For the sake of the analysis. Vol. Hydro One and OPA web-sites [65]-[67]. Genco-3 is considered to own 19 generating units with a total capacity of 15.400 MW with a diverse supply mix of coal-fired thermal (580 MW). genco profiles are constructed that approximately match the total installed capacity in Ontario of 25. 2008.600 MW) units. Genco-1 and genco-2 are assumed to own 9 generating units each. pp. These generating units are considered to be owned by three different gencos for the purpose of the coordinated maintenance scheduling problem. Nov. The transmission specific data is obtained from the IESO. 1871-1882. hydro (1690 MW) and nuclear (11. these are fairly generic in nature and can be easily replaced by actual data. A total of 37 generators are considered. The individual genco specific data has been constructed by the author. However. if available.1.Chapter 4 Security Coordinated Maintenance Scheduling in Deregulation Based on Genco Contribution to Unserved Energy: Ontario Based Example 1
4. gas-fired (1530 MW).620 MW. 4. 220 kV and 115 kV voltage levels is used for the coordinated production and maintenance scheduling studies discussed in Chapter-3.1 Ontario Based Example: Data Acquisition and Processing
A 57-Bus Ontario power grid system considering 500 kV. 23. No. Barot and K.

1.The data pertaining to their maintenance duration and number of units to be on simultaneous maintenance are designed based on the practices adopted in IEEE Reliability Test System Data [68. These prices are used to derive the appropriate medium-term price duration curve 40
.5 Price Information from Ontario Market The weighted monthly average of the peak Ontario Hourly Energy Price (HOEP) for the year 2004 is taken [65] as the base-price to define the price of energy (ρ) in the security coordinated maintenance scheduling model.3 Assumptions For the proposed coordinated maintenance scheduling scheme. 220 kV and 115 kV lines is used. The ISO has information on average production costs of all generators (supplied by gencos).2 Network Data of Ontario The transmission network of the Ontario system covering the 500 kV. each spanning one month. 2. A brief summary of the transmission system data is given below: Total number of buses = 57 Buses with generators connected = 13 500 kV buses = 13 220 kV buses = 28 115 kV buses = 16 Total number of transmission lines = 159 500 kV lines = 16 220 kV lines = 78 115 kV lines = 65 4. the following assumptions are made 1.1. 69]. Gencos are mandated to abide by ISO’s instructions when system reliability and security are the issues (when there is unserved energy in the system). 4.4 Time Period of Medium-Term Operations Problem The time-horizon for the medium-term operations and maintenance scheduling scheme under consideration is one year.1. Intermediate and Peak load sub-periods based on the electricity demand in the system 4. The month again is sub-divided into Base. 4.1. This horizon is divided into 12 periods.

1 Average Peak Monthly HOEP in 2004
41
.2 from which monthly Load Scaling Factors are derived and applied to a bus-wise annual peak demand-data obtained from [65]. between $2.7 Ontario System Demand The actual month-wise total energy demand of Ontario for 2004 is shown in Fig. which could be from expensive generation sources (such as diesel generators) or the payment that the ISO makes for interrupted power. This gives the bus-wise monthly peak demand data for the whole system. Fig.
100 95 90 85 80 75 70 65 60 55 50 1 2 3 4 5 6 7 8 9 10 11 12 Month of Year
4.250/MWh during peak load sub-periods. Thereafter. a second scaling factor was applied to derive the month-wise intermediate and base demand data for every bus.250/MWh to $3.1 shows the average monthly peak HOEP variation in the year 2004. 4.
Price.6 The Cost of Unserved Energy (Cn) The cost of unserved energy (Cn) typically represents the cost of substitute energy.750/MWh to $6.4.500/MWh to $2. In this work we have considered Cn to be varying between $1.for peak.750/MWh during intermediate-load and between $3. intermediate and base load conditions.1. 4.500/MWh over the 12 monthly periods for base-load. $/MWh
Figure 4.1.

There are four generator buses (buses-4000. These generators in set kL.2. consider the common pertaining to p=9.1.2 Initial and Final Maintenance Schedules The initial maintenance schedules for each genco are obtained by individually executing the GMS program. In Table-4.7105} = {7300 .2. Section-3. which was obtained after the coordination scheme converged after five iterations. The final security coordinated solution is obtained after five iterations and it provides the maintenance schedules of each genco.1 for the Ontario system data used for the studies.6400 . Hence. the set of generating units accountable for the bus-wise and total unserved power for period m is determined. The second column represents the set of generator buses kL (kL ∈ KU) corresponding to a common Cp.2 Results and Discussions
Based on the mathematical formulation of the security coordinated maintenance scheduling scheme discussed in Chapter 3.2. 43
.4.U2 and U3 (as given in column-3).1. Using the same argument. 7105) which form the set kL corresponding to p=9. maximizing their respective profits. and using the case-study data presented in Section-4.{4000 . 4. This set of load buses form the common Cp. 4. p denotes the index of the common in the first column.6401.2 the initial maintenance schedule as obtained by genco-1 from its GMS program is given and then the final coordinated maintenance schedule is provided. For example. 6401.4.1 Genco-1 Maintenance Schedule In Table-4. which is further used to synthesize the corrective signals as described in Section-3. 6400.2.4. verified by the ISO.7108}
In simple words. Column-4 corresponding to p=9 indicates the set of load buses which are supplied uniquely by set kL. we can state that load buses 7300.2. as well as their corresponding medium-term production schedules.7100 . This set (kL) is found by first determining the domain list for all generator buses and then grouping the set of generator buses contributing to all load buses.2. we can write:
C9.kL. detailed simulation studies are carried out and the results are discussed in this section. belong to gencos. 4.kL.1 Calculation of Commons Table-4. 7100 and 7108 are uniquely supplied by generators connected at buses in set Kl.1 shows the commons calculated using the ALLOCATE algorithm described in Chapter 3.

2.3).2 Genco-2 Maintenance Schedule The initial maintenance schedule of genco-2 (Table-4.3) and understandably the genco seeks to maximize the utilization of its hydro generation. Units on MW Maintenance 0 800 9 800 9 1450 3. The ISO coordinated schedule. Units on MW Maintenance 0 800 9 1800 6.3 Initial and Final Maintenance Status of Generators in Genco-2
Period 1 2 3 4 5 6 7 8 9 10 11 12 Initial Maintenance Schedule MCAP. Fig. From its final coordinated maintenance schedule (Table-4. Table 4. 8 700 8
46
.5 Coordinated Maintenance Schedule MCAP.2. 4.4.2.5 1000 7 1700 7.6 1000 6 0 0 0 2000 1.000 MW of capacity is now on maintenance in period-9 although periods 6-8 still do not have any unit on maintenance. can therefore be inferred.8 1200 4.4.9 2000 6.3) shows that no generator is on maintenance during periods 6–9 because of the high availability of hydro energy during these months (see Fig. emphasizes more on maintenance during low demand months (4-5 and 9-11) when market prices are also low.7 1000 7 0 0 0 0 1500 1.8 1150 3.2.5 shows βu (for u = genco-2) for both the initial and final maintenance schedules. it is seen that 2.4.

is not desirable because that results in shortage of power in those periods.3 0.4) that the maintenance of nuclear units.2. 16.200 MW capacity and other 4 units (units-8 to 11) each of 800 MW capacity.2 0.05 0 1 2 3 4 5 6 7 8 9 10 11 12 Month of Year Initial Beta -Genco 2 Final Beta -Genco 2
Beta
Figure 4.600 MW.2.3 Genco-3 Maintenance Schedule In case of genco-3. Note that. underwent a significant shift of periods. It is seen that the large nuclear units-14.5 Fractional Capacity on Maintenance for Genco-2
4. which is made up of 7 units (units-12 to 18) each of 1.4 0. Note that nuclear generation capacity in genco-3 is 11.0. as per the initial schedule. two nuclear units are always on maintenance between months 4 and 9. 17 and 18 are on maintenance during the months 6-9.15 0. it can be noted from a comparison of the initial and final schedules (Table-4.35 0.25 0. as in the initial schedule.1 0.
47
. Such a clustering of the maintenance of large units during specific periods. four nuclear units are on maintenance. particularly. and in month-12.

high energy prices are usually driven by high energy demand in the system and hence from the ISO’s perspective as well. since they seek to maximize their profit. The security coordinated maintenance schedule also retains the same trend and no generator is on maintenance in January. no generator is scheduled for maintenance in January. This is because. the security coordinated maintenance schedule results in adequate generation capacity and a fairly levelized profile of reserves at all months. translates to the flattening of β. there will be peak deficit in the system in some periods. discussed earlier. the OCP also seeks to schedule it maintenance at low demand (and hence low price) periods.4.2. month-6 has a very low reserve available. If the initial maintenance schedules of gencos are implemented without coordination with the ISO.8 shows the resulting system reserves in the two cases. the gencos are reluctant to schedule (through GMS program) any unit on maintenance in January.2. Because of this correlation between market price and system demand. This flattening of the system reserves profile.
49
. 8 and 12 is higher than system capacity available.2. The coordination approach therefore provides very satisfactory results and is simple. This is attributed to over maintenance commitments by gencos during these months. Therefore. It is seen from the figures that after the initial solution. Also. although the gencos and the ISO have different objectives.2. implying a negative reserve condition in the system.4. 4.5 Capacity Available and Peak Load Figure 4. peak demand for months 7. This suggests that the coordination process in maintenance scheduling is very critical in deregulated electricity markets from system operational security viewpoint. and is a desirable feature achieved through the coordination scheme.4 Other Observations An interesting observation is that the energy price in January (period-1) being very high (∼$100/MWh). Thus the OCP acts in the same direction as the individual genco’s GMS programs. On the other hand. they do not conflict or contradict each other.7 shows a month-wise comparison of peak demand and system capacity after the initial and coordinated solutions while Fig . logical and fair to all gencos.

is termed as the Base iteration. It is also understandable that the gencos’ profits will decrease with OCP iterations. whereas the system cost is significantly reduced to the order of 77. The first OCP run.7 System Demand and Total Capacity Available from Initial and Coordinated Maintenance Schedule
4. and hence the profits were at their maximum. without any system constraints.
50
. The significant reduction in total system cost is attributed to the reduction. The profits thereafter decrease because the gencos have to modify their maintenance schedules as additional constraints are imposed by the ISO. A feasible solution refers to the case where there is no unserved energy at any bus. The Base iteration was the case when each genco maximized its profit. It is seen that the profit of the individual gencos are reduced marginally from the Base solution to the final security coordinated solution.6 Costs and Profits We also examine the total system cost and the net profit of each genco as the OCP iterative process progresses. based on initial submission of maintenance schedules from gencos. The system cost and the genco profits are given in Table-4. Thereafter it took five iterations for the process to converge to a feasible solution. MW 23000 21000 19000 17000 15000 1 2 3 4 5 6 7 8 9 10 11 12 Month of Year Initial Available Capacity Final Available Capacity Peak Load
Figure 4.5.623%.5%. The highest reduction in profit is for genco-3 by 0.2.2. and finally.27000 25000 Capacity. elimination of unserved energy from the system as the coordination process progresses towards convergence.

in every iteration. Note that in the Coordinated PS. these PS are not practicable. γ. c) Coordinated PS. security coordinated and implementable by gencos. MW Genco Genco Genco 1 2 3 2335 2280 1680 2260 200 880 3500 900 2200 1650 2900 1100 3400 -
Base 1 2 3 4 5
Figs. b) Final Genco PS. Table 4.that obtained from the OCP by the ISO after the coordination scheme has converged.2. 4.9). Hence after the convergence of the OCP.that obtained from GMS program by individual gencos based on profit maximizing maintenance scheduling without considering any ISO intervention or coordination. feasible. On the other hand. whereas the first two are obtained from the genco’s perspective of profit maximization without due consideration of the demand. for the gencos. In the case of genco-1 (Fig. 4.that obtained from the GMS program by individual gencos which leads to the convergence of the coordination scheme. the OCP outputs a set of PS from the overall system energy-supply balance perspective. seeking to minimize the total system cost subject to security and other system consraints. units are less utilized during the base sub-period as compared to intermediate and
52
.11 shows a comparison of three PS cases for each genco as discussed below: a) Initial Genco PS. it is seen that the Initial Genco PS and the Final Genco PS are somewhat different from the Coordinated PS essentially because the later takes into account the balance between the system demand and supply.4. the PS generated thereby is practical.3 Production Schedules An outcome of the GMS Program for a genco is its medium-term production schedule (PS) along with its maintenance schedule but since the gencos seek to maximize the net profit without considering the system demand.6 Corrective Signals for Gencos
Derived after Iteration Period in which corrective signal is applied 7 8 12 6 2 3 None Corrective signal (maximum allowable capacity on maintenance).9-4.

The PS shows that utilization of hydro resources is fairly consistent throughout the year for all the cases. It is not advisable for such a utility to schedule its units for maintenance during high hydro availability months. This is because genco-1 has the highest operating costs amongst the three utilities and hence is not utilized as much for the base load. Interestingly. 4. which is a hydro-based utility with gross capacity of 5950 MW. a similar analysis is presented for genco-2. GWh
3500 3000 2500 2000 1500 1000 500 0
Final Genco
Coordinated PS
1 3 5
7 9 11
2 4 6 8 10 12 Month of Year Base Inter Peak
1
3 5 7 9 11
Figure 4. The increase in base load generation in the Coordinated PS is to balance the reduction in base-load generation of genco-1.9 Comparison of Various Production Schedules of Genco-1 (Total Capacity = 4. the base-load generation is somewhat increased in the Coordinated PS as compared to the PS determined by the genco itself (Initial PS and Final PS). 7 and 8 because of the high hydro energy availability during these periods.peak.10. This is also true from ISO’s viewpoint. because hydro generation is cheaper than any other source. This genco also operates as an intermediate and peak-load utility with very little base-load generation. Note that the total production from genco-2 attains a peak during months-6. and its PS is generally constrained by water availability over the year. Initial Genco
Energy Production.9. observed in Fig.270 MW)
In Fig. 4.
53
.

Table-4. The CPLEX solver is very efficient to handle such optimization models. The whole scheme is solved on a standard Intel Xeon processor with 3 GB RAM. the details of the computational burden involved in the coordinated maintenance scheduling scheme is discussed.601 442.750 1.7 Computational Details of Optimization Problems
Event Equation Blocks Variable Blocks Single equations Single variables Non zero elements Discrete variables Model Generation time(sec) Model Execution time (sec) Genco-1 GMS 10 5 1.
4. All the GMS programs pertaining to individual gencos have 10 equation-blocks representing the various constraints. For example.338. The case study approximates the Ontario power system.170 1596 0.047 OCP 9 4 1. month-12 which had a low initial scheduled generation has a higher schedule in the Coordinated PS. The detailed mathematical formulation and the coordination scheme are proposed in Chapter 3. The OCP is a fairly large-scale linear programming model with a large number of constraints.286 756 0. The GMS programs are linear mixed-integer optimization models and are solved using the CPLEX solver in GAMS [70] environment.885 17.281 11.19 17.047 0.031 Genco-2 GMS 10 5 1. This model is also solved very efficiently using the CPLEX solver in GAMS environment. arising because of the transmission limits at multiple voltage levels and other constraints. a detailed case study is presented to demonstrate the application of the security coordinated approach to generator maintenance scheduling problem in deregulation. can be attributed to alteration of maintenance schedules.A careful study reveals that the small changes between the initial and final PS.031 0.081 5.538 756 0.858 1.657 2. Three gencos are considered which are assumed to be players operating in the competitive electricity market 55
.3 Computational Details
In this sub-section. for a few of the periods.7 provides the details of the size of the mathematical models.699 2. as a simplified 57-bus representation. Table 4.081 5.389.21
4.4 Concluding Remarks
In this chapter.015 0.031 Genco-3 GMS 11 5 3.

The ISO coordinates the maintenance schedules and also arrives at an optimal medium-term production schedule that takes into account system security and other relevant system constraints. The scheme has the advantage of being fair. understandable and simple. logical. and tries to retain these schedules as far as possible. The proposed scheme is very efficient and converges within five iterations. to request for their modifications.
56
. unless it is absolutely important from system security considerations.environment and operating with profit maximization objective. It also takes into consideration the gencos’ individual maintenance schedules.

affected by such variations. whether the reliability of the load service provided by the utility varies across the system from bus to bus. Bhattacharya. a new approach to determine bus-wise Load Service Probability (LSP) indices in power systems is presented. by the ISO was presented. using this index. while it is 23. bus-wise load distribution. These LSP indices are arrived at by defining and computing. The LMPs would vary across the system buses because of the system load pattern. one can precisely state that the LSP at bus-15 is 23. Transmission and Distribution. congestion on certain transmission lines or transmission losses. In such a case. Load service probability differentiated nodal pricing in power systems. The bus-wise LSP indices are thereafter utilized to formulate a novel proposition for LSPdifferentiated LMPs for electricity markets.
57
. how the LMPs.3.Chapter 5 Load Service Probability Differentiated Nodal Pricing in Power Systems 1
5.5 hours on a given day. In this chapter another important question is addressed – that of – whether there is a need to consider the issue of customer’s locations in the power system when the utility provides service to them. Barot and K. in revision. Now. The proposed bus-wise LSP indices vary across the system buses because of differences in contribution of individual generators to serving the load at a given bus.2 hours at another bus-17. In other words.1 Introduction
In Chapters-3 and 4. bus-wise LOLP (LOLPi) indices. gencos and ISO. on the same day. the LMPi should be appropriately scaled to factor in the LSP so that the customers
1
Some parts of this chapter has been submitted for publication in• H. Furthermore. for a given bus i. as explained in Section-5. In this Chapter. For example. the LMP variations across a set of power system buses are compared with the proposed bus-wise LSP indices. one of the important medium-term operational issues of production-cummaintenance scheduling and its coordination amongst several gencos.and if so.3. Such bus-wise LSP information can be very valuable to customers. LMPi can be very high while LSPi can be low which would indicate more chances of outage at bus i. which are determined from market auctions. It also answer the important question of how the LMPs be differentiated by the load service probability so that it is fair to all customers. IET Proceedings on Generation.

which is a linear programming model of the system and determines the power flows for a given load condition while ignoring the reactive power flows and voltage constraints. Using this information.4 presents a case study and discusses the results so obtained.located at bus-i are fairly priced. On the other hand. The rest of the chapter is organized as follows: in Section-5. be used by the ISO.5. for large systems.
58
. as appropriate.
5. Section-5. In this thesis. Section-5. only active power flows are sufficient.2 The Proposed Load Service Probability Index
In order to determine the bus-wise LSP indices. particularly. Such detailed OPF computations can be very involving. It is assumed that individual gencos would provide the ISO with information on their respective generating unit availability status.1. Moreover. the OCP presented in Chapter 3 has been used. denoted by LOLPi. linear power flow models can as well. having a significantly low LMPj but enjoying a high value of LSPj should be charged a higher price. Therefore. the ISO executes an OPF program to compute the power flows and transmission line loadings for a given load condition. using the scheme shown in Fig. for the sake of LMP calculations.2 an overview of the proposed scheme is presented.5 provides the concluding remarks of the chapter. customers at a bus j. simpler. a set of bus-wise LOLP indices are computed.3 discusses the concept of locational LSP while Section-5. first.

Figure 5.1 Schematic Overview of Computation of Bus-wise LSP

Using the transmission line power flows determined from the OCP, the ALLOCATE algorithm presented in Section-3.4.2.1 is executed to obtain the domains and commons for the system. (The explanation for domains and commons is given in Section-3.4.2.1). Using the domains and commons, the set GRi is determined, which represents the group of generators responsible for supplying the load at a bus i. The set GRi and the power flow information obtained from OCP are used to calculate the contribution of generators to loads [60]. The ISOLATE algorithm determines the contribution factors of generators (discussed in Sectio-5.3.2) and hence arrives at an isolated bus representation of the system, assuming the load to remain constant for the period. The last step in the proposed scheme is the CONVOLVE algorithm which is applied to each isolated load bus to calculate the cumulative outage probability of generators supplying a load at bus i and hence to determine LOLPi. The bus-wise LSPs, i.e., LSPi are easily computed once LOLPi are determined, as explained in the next section.

59

5.3 The Concept of Locational Load Service Probability
5.3.1 Domains, Commons and the ALLOCATE Algorithm The concept of domains and commons was proposed in [60] and explained in detail in Chapter 3, to determine the share of generators to the load being served. The ALLOCATE algorithm, presented in detail earlier, is used to determine the domains and commons. The commons also help in finding the contribution of a generator to a particular load making use of proportionality assumptions. The following terminologies and definitions are explained below, which were first introduced in [60]: • • • Rank of common- denotes the number of generators supplying a specific common i.e. if two generators supplies a common then rank of the common is 2. The transmission lines can be classified as either being internal to a common or external to a common. Link- the set of external transmission lines connecting same commons. o Power flow directions in all transmission lines constituting a link, are always same. o The power always flows from a common of lower rank to a common of a higher rank in a link. • The total power injection in a common is called the inflow of the common while the total power extraction (loads and power flows to other commons of higher ranks) is termed as outflows from a common. It can be argued that if a set of generators Gri is responsible to serve the load at bus i, then Gri is also responsible for any load that remains unserved at bus i. Therefore, if any generator belonging to Gri experiences a capacity outage, there will be some unserved energy at bus i proportional to the capacity on outage, from within the set Gri. 5.3.2 Isolated Bus Representation of System In an integrated power system, generators connected to generator buses supply various load buses through a mesh of transmission lines. The power delivered by each generator reaches a specific set of load buses, depending on the electrical properties of the available paths for power transmission. Let us consider a generator G connected to generator bus g and having a capacity of P MW. From the principles of Kirchhoff’s Laws and applying the concept of domains it can be determined that G supplies some load at specific buses, say, buses-1, 4, 5 and 6, for a given system condition. Therefore, it can be stated that the power P generated by G was shared by the loads at buses 1, 4, 5, and 6 in a 60

certain proportion. If the load at bus-6 receives a% of P, we can assume that a generator of capacity (a*P/100) MW is instead connected at bus-6 and not at bus g. Extending the same principle, assume that the load at bus-6 is supplied by three generators of capacities P1, P2 and P3 (connected at some generator buses in the system), in proportions of a1%, a2% and a3% respectively. Then bus-6 can be considered to exist in isolation with three generators connected to it, with respective reduced capacities of (a1*P1/100), (a2*P2/100) and (a3*P3/100) MW (Fig. 5.2). The integrated power system can therefore be viewed as a system of isolated load buses, each having a group of generators of proportionally reduced capacities, supplying the load locally.

Figure 5.2 Isolated Bus Representation

5.3.2.1 ISOLATE Algorithm When the domains and commons are determined for a given state of the power system, the electrical power system can be represented by a state diagram [60]. In the state diagram, the commons are represented as nodes and links are represented as branches with power flows that are in the direction from a common of lower rank to a common of higher rank. Therefore the state graph is always a directed graph that is acyclic in nature (no closed path of flows). Using the state graph and the power flow information available from OCP, the contribution of generators to total outflows from a common is determined. The total outflows is the total load on the member buses of the common plus the power flowing out of a common to other commons of higher rank. Using the above calculated contribution of generators to total outflows, the contribution of generators relative to their own generation levels can be computed. This is used to allocate the reserve capacity of a generator to different commons and then to different load buses within the common to 61

Bus 6

Let Pg. which is the sum of power flowing out to other commons of higher rank and the total load of the common j. Let Ij be the inflow to the common j. p + ∑ PDi
p i i∈ j
(5.p = ⎜ ∑ Pp. The complete algorithm is described below. Let Pg be the power generated by generator g and PgMax be its generating capacity. j Ij
∀ g ∈ Gri
(5. Then. p =
j
Ip
∀ g ∈ Gri
(5. p = C g .
C g.3.finally arrive at the isolated load bus representation. the relative contribution of generator g to the inflow or total outflow of common j is given by. p be the power flow over link between common j to common p (from j to p). j =
AC g .
I j = ∑ P j .m + ∑ PDi ⎟ ⋅ C g.
Pg .4)
In (5. j . R g =
Max Pg
∀ g ∈ Gri
(5. and is depicted in Fig.2)
ACg. Then. p
∑ Pg . p = Power flow over links from common j to common p PDi = Power demand at load bus i in common j Then. p
and given by:
∀ g ∈ Gri
(5.5. j . p C g. the absolute contribution of generator g to common p is given by:
⎞ ⎛ ⎟ ⎜ AC g.3)
The contribution of generator g to the inflow or the total outflow of common p is denoted as Cg. j ∗ P j .1)
Where.p ⋅ R g ⎟ ⎜m i ⎟ ⎜ i∈ p ⎠ ⎝ where.5)
Pg
62
. Pj. j.4) Ip is the inflow to common p. due to generator g. j is the absolute contribution of generator g to inflow of common j.

p ⋅ R g
i ∈ p. It is assumed here that the bus load remains unchanged during the period under consideration.5) proportionately allocates reserves available from a generator g to a common p. Considering a security constrained system (i.i is the synthetically reduced capacity (SRC) of generator g (g Є Gri) at load bus i in
common p.5) to:
SRC Pg . The set Gri does not have any reserve capacity available or the capacity outage is more than the reserve capacity available. the LOLPi indices can be formulated for a bus i. it is also the contribution of generator g to every load bus in common j and henceforth generation capacity at each load bus can be obtained by reducing (5. if line limits are not violated. the bus-loads are assumed to remain unchanged for the 5-minute interval under consideration.e. then the bus load is assumed to remain unchanged during the hour.3.Equation (5. there is some capacity outage. On the other hand. These indices are determined using the cumulative outage probability table of SRC generators. Consider a power system where generators are available as per their commitment status known a priori. The load at each isolated load bus is met locally by a corresponding set of SRC generators. For example. Now from the proportionality assumption. the load at bus i will not be served. the entire power system can now be represented by a set of isolated load buses. if the LMPs are determined 5-minutes ahead. the following events may take place: 1) 2) The set Gri has some reserve capacity available and it can supply the load at bus-i by increasing its contribution. g ∈ Gri
(5. i = PDi ⋅ C g .6). The LOLPi indices can thereafter be determined taking into account the Forced Outage Rates (FORs) of these SRC generators supplying each bus. Using this rational. depending on their individual contributions to the load.. if the LMPs are calculated hourly. as in Ontario. from the isolated set of generators Gri responsible for supplying the load at the bus i. Pg . line limits are enforced). This generation level may be equal to or less than a generator’s maximum generation capacity. supplying load at bus i.3 Locational Load Service Probability Indices As per the procedures described so far. 64
. If. if Xgj is the contribution of generator g to common j. Gri. Gri. 5.6)
SRC In (5. all the generators will generate power at their respective “scheduled generation levels”.

7).3.1 LOLP Convolution Algorithm and Calculating LOLPi The computation of LOLPi is carried out using the well known generating unit convolution algorithm [38] to develop the cumulative outage probability table.10)
As mentioned earlier. The LOLPi is calculated for a value of X0 that is the difference between the sum of capacities of SRC generating units in Gri and the load at the bus i.3. The convolution equations are given as follows:
CPROBiNew(X)= CPROBiOld (X)* (1-FORn ) + CPROBiOld (X-C)*FORn CPROBiOld (X-C) = 1 ∀ (X .
LOLPi = CPROBiNew(X 0 )
(5.C) ≤ 0
(5. pertaining to the load bus i) instead of the total set of generating units with their full capacities.3. the LSP provides information to the ISO.7)
In (5. LOLPi can be determined. This information can be effectively integrated with the LMPs determined from energy market clearing to arrive at locational LSP differentiated nodal prices for the power system 5. referred to as LOLPSystem in this chapter to distinguish it from LOLPi. and FORn represents the forced outage rate of unit n. it should be noted that the main difference in the construction of the outage table is the use of Gri (the set of SRC generators.3.3. The LOLPSystem can be determined using the CONVOLVE algorithm for
65
.
SRC X 0 = ∑ Pg . i − PDi g
g ∈ Gri
(5.5. during the given period of market settlement. customers and other market players as to what is the probability that the load at a bus i will be served.4 Differential Locational Load Service Probability Let us now refer to the classical system-level LOLP.2 Locational Load Service Probability (LSPi) The bus-wise LSP. C is the capacity of the next generating unit n being convolved. From the cumulative outage probability table. can be computed from LOLPi using the formula:
LSPi = 1 − LOLPi
(5.9)
5. LSPi. However.8)
Where. CP is the cumulative outage probability of X MW or more of generating capacity on outage. assuming the load at bus i to remain constant for the period of study.

assuming all generators are available. Therefore. the customers are charged lower than the market determined LMPi. A reverse scaling approach of the LMPs with respect to ΔLSPi is proposed. There can be other applications and usefulness of LSPi. we define:
ΔLOLPi = LOLPi − LOLPSystem
(5.13)
From (5.the total system demand. indicates the probability of not serving the load at a bus as compared to the probability of not serving the total system load.5 LSP Differentiated Nodal Prices
(5. On the other hand.13) it is observed that customers at buses with higher probability of load being served (ΔLSPi< 0) are charged a higher price than the LMPi determined from market clearing.3.11).11)
The differential LOLPi. the LMP at a bus needs to be suitably adjusteddownwards.
ˆ LMPi = LMPi (1 + ΔLSPi )
(5.
ˆ denoted by LMPi is given by (5. Consequently.12) denotes the probability of serving the load at a bus as compared to the probability of serving the total system load. and therefore the LMP at that bus needs to be suitably adjusted upwards.12)
From Section-5. It should be noted that in this chapter a simple method is used to demonstrate how the bus-wise LSPi can be synthesized with the LMPs.4 the ΔLSPi values are obtained for every bus in the system.3. at those buses where the probability of load being served is lower (ΔLSPi > 0). The ΔLSPi in (5. ΔLSPi. it indicates an enhanced load serving probability at the bus.13) below. and hence arrive at LSP differentiated LMPs. compared to system LSP. It is proposed that the LMP at a bus be appropriately adjusted by using the ΔLSPi values. A positive value of ΔLSPi at a bus indicates a deteriorated probability of serving the load at a bus as compared to the system LSP. we can define the differential LSPi as. such as in power system planning where such locational 66
. Once LOLPSystem is computed by the ISO. as follows:
ΔLSPi = (1 − LSPi ) − (1 − LSPSystem ) = LSPSystem − LSPi
5. when ΔLSPi is negative. The LSP differentiated LMP. Similarly. taking that as a reference. defined by ΔLOLPi in (5.

5} of common C3. It can be observed that the power flow directions are from nodes (commons) of lower ranks to nodes of higher ranks. However. 4. node-2 of rank = 2.4. For example. Note that in 5-bus system we have 3 commons with different ranks and no two commons have same rank. The configuration of the 5-bus test system and the associated data are provided in the Appendix.08. The state graph has 3 nodes. as given in Table-5. no information is available as to how much these generators contribute to the loads.
5. let us consider common p=3. Hence the state-graph is termed as a directed and acyclic graph. From the system configuration. 2.08. The directed acyclic state graph was now developed for the commons obtained in Table-5.
67
. The three generators connected at bus-1. until this point. U2.4. each representing a common and has generation sources.5. There is a need for further research in this area to investigate how ideally the LMPs are scaled taking into account the LSPs. it can be seen that at these generator buses three generators are connected: {U1.1 5-Bus Simple Power System Case Study The proposed concept of LSP indices and hence the LSP-differentiated LMPs are now calculated for a simple 5-bus test power system to understand the steps and the methodology in a clear manner. FOR2 = 0. The unique set {kL} of generator buses {1. kL. The levels are ordered in ascending order of their ranks.indices can act as a signal for investments. as shown in Fig. The nodes in the state-graph are arranged in various horizontal levels.1. 4 and 5. and node-3 of rank = 3.1. node-1 is a common of rank = 1. U4}. each level representing commons of same rank.4 Case Study
5.1. as denoted by the bold incoming arrows. An OPF is executed to obtain the power flow information for the system and then the ALLOCATE algorithm is applied to determine the commons for the 5-bus test system. bus-2 and bus-4 have forced outage rates as follows: FOR1 = 0. As an example. 4} supplies the member load buses {3. FOR4 = 0. Hence these three generators are responsible for supplying the load at buses-3. Node-1 is the root node for the power flow.

1 List of Commons in the 5-Bus system p 1 2 3 Set of generator buses (kL) Rank 1 1 1.4 3 Common Cp.Table 5. From these contributions. the contribution of each generator to the loads and outflows of a common is determined. kL 1 2 3. bus-4. to demonstrate the results (Fig 5. Power Generation and Links Connecting to other Commons
5.4 State Graph of 5-Bus System Showing Commons. We have presented one sample load bus.1. a relative share of generation capacity is computed in order to arrive at the Isolated Bus Representation for each load bus.2 2 1.5).2.1 Isolated Bus Representation Using the state-graph.
68
.4.4.5
Figure 5.

Therefore.5 Isolated Bus Representation for Bus-4 in the 5-Bus Test System
5.6 shows the variation of cumulative outage probability for different MW blocks or more of generation capacity on outage at bus-4.34 – 215 MW = 59.Figure 5. Therefore. Fig.5. from (5. the total SRC of the set Gr4 is 274. at bus-4.2 Determining Locational LSP Indices and LSP-Differentiated LMPs The CONVOLVE algorithm was applied to determine the cumulative outage probability of the three SRC generators supplying the specified load at bus-4. At bus-4.4.23824.9). as seen in Fig.34) corresponds to the cumulative probability of 59.6. an outage of X0 = 274.34 MW or more on outage.34 MW or more will result in load not being served at bus-4. which is 0. LOLP4(59.1.5.34 MW and the load is 215 MW.
69
.

5.23824. for three of the system buses.7 and Fig. For rest of the buses. The consequent effect of the bus-wise variation in LSPs is seen in the computation of LSPdifferentiated LMPs. It can be seen in Fig.6 59.7.8 shows the locational LSP indices for all the buses in the system along with the system LSP for the sake of comparison.6 Cumulative Outage Probability at Bus-4 of the 5-Bus Test System having 3 SRC Generators Accountable for Supplying its Specified Load
Now.5. is the LOLPSystem. bus-1 and bus-2 have significantly lower LOLPs or higher LSPs compared to that of the overall system.2 Cummulative Probability of Outage 1 0.e.5.1. It is seen from Fig.9 that the LMPs at bus-1 and bus-2 are increased from their base-case values. which is found to be 0. namely bus3. the LOLPSystem is determined for the 5-bus test system considering the total available system generating capacity of 1.5. i.
70
. The LOLPi(X0) for all load buses in the 5-bus system and LOLPSystem are plotted in Fig. On the other hand.6 150 175 200 X or more MW on outage Cummulative Probability
Figure 5.8 that the LOLPSystem and the system-LSP coincides with the bus-wise LOLPs and LSPs respectively. Fig.8 0. The cumulative probability of outage of X0 = 1. 4 and 5..100 MW supplying a total load of 810 MW.6 0.8 75 100 140.100 – 810 MW. of 290 MW or more.34 61.4 0.2 0 0 25 44. because the LSP at these buses are higher than the system-LSP. there is no change in the LMPs from their base-case values because the LSP at these buses is exactly the same as the system-LSP.88 71.5.

U37. The transmission network of the representative Ontario power system was used. U27. U313.2.1 System State Graph and Generator Contributions On executing the OCP and applying the ALLOCATE algorithm. The analysis reported here is carried out considering a specific load condition on the system that remains constant for the duration of one hour.2 57-Bus Ontario Based Example The 57-Bus representative Ontario power system which was considered in Chapter-4 is considered for this study. U315. 3108. As an example. U314. U317.7 6 5 LMPs. U310. The total capacity in the system is 25.4. let us consider common p=15. $/MWh 4 3 2 1 0 1 2 3 Buses in the System Base Case LMPs LSP Differntiated LMP 4 5
Figure 5. The data pertaining to their outages i. U311. 6401} supplies the member load buses {3107. it can be
determined that at these generator buses the following eighteen generators are connected: {U26. 3108 and 4105. 5.2. U35.620 MW and it approximately matches the current total installed capacity in Ontario. 6400. A total of 37 generators spread over 13 generating buses are considered. U38. U39. U36. 5105. their FOR data were designed based on the practices adopted in IEEE Reliability Test System Data [68]. U318. U319}.
kL. The unique set {kL} of generator buses {4000. Hence these 18 generators are responsible for supplying the load at buses-3107. 4105} of common C15.e.
From the system data. 4105. U34. the commons for the representative Ontario power system are obtained as given in Table-5.9 Comparison of Base Case LMPs with LSP-Differentiated LMPs
5. 5102. 72
.4. U312. U316.

However, until this point, no information is available as to how much these generators contribute to the loads. Similarly, for p=19 it can be observed that bus-101 is being supplied by a group of generators that are connected to 9 generator buses {101, 1106, 2007, 4000, 4105, 5102, 5105, 6400, 6401}. From system data, we know that there are 27 generating units actually connected at these 9 generator buses. Similarly, for p=1, it is observed that bus-2007 is being uniquely supplied by the generator located at bus-2007. The directed acyclic state graph was therefore developed for the commons obtained in Table-5.2. The graph is shown in Fig.5.10. The state graph has 19 nodes each representing a common. Out of these 19 commons, 13 of them have generation sources, as denoted by the bold incoming arrows. The nodes in the state-graph are arranged in various horizontal levels, each level representing commons of same rank. The levels are ordered in ascending order of their ranks. For example, nodes 1, 2, 3, 4 and 5 are commons with rank 1. They are the root nodes for the power flows. Similarly, nodes 6 and 7 have a rank of 2 while nodes 8, 9, and 10 have a rank 3 as shown in Table-5.2 and in Fig.5.10. Lastly node 19 has the highest rank of 9 in the state graph. It can be observed that the power flow directions are from nodes (commons) of lower ranks to nodes of higher ranks. Hence the stategraph is termed as a directed and acyclic graph. 5.4.2.2 Isolated Bus Representation Using the state-graph, the contribution of each generator to the loads and outflows of a common is determined. From these contributions, a relative share of generation capacity is computed in order to arrive at the Isolated Bus Representation for each load bus.

Figure 5.10 State Graph of the 57-Bus Ontario Based Power System Showing Commons, Power Generation and Links Connecting to Other Commons

In this chapter we have presented two sample load buses, bus-3107 and bus-2007, chosen arbitrarily, to demonstrate the results. It was seen that the isolated bus representation for bus-3107 involved 18 SRC generating units while that for bus-2007 involved 3 SRC generating units, as shown in Fig. 5.11. The associated capacities of the SRC generators connected to the isolated buses are also labeled alongside. The ‘ring’ structure of the isolated bus-3107 has been used for the purpose of accommodating and depicting the 18 SRC generating unit connections at the bus.

75

4). Similarly. the total SRC of the set Gr3107 is 619.3 and 5. for bus-2007.9 MW or more will result in load not being served at bus-3107. which is 0. the total SRC of the set Gr2007 is 673.88 – 540 MW = 79.9) corresponds to the cumulative probability of 79. an outage of X0 = 673. at bus-3107. an outage of X0 = 619.4 respectively.24) = 0.88 MW and the load is 540 MW.111622 (from Table-5. in Tables-5. LOLP3107 (79.24 – 540 = 133.9 MW or more on outage.3).Figure 5.11 Isolated Bus Representation for Bus-2007 and Bus-3107 of the Ontario Based Power System
5. LOLP2007 (133. from (9).2. At bus-3107.
76
. Therefore.3 Determining Location LSP Indices The CONVOLVE algorithm was applied to determine the cumulative outage probability of the 18 SRC generators supplying the specified load at bus-3107.24 MW or more will result in load not being served at bus-2007. The corresponding LOLPi for both buses 3107 and 2007 are shown by the rows in bold. Hence. Therefore. Table-5. Therefore. and the 3 SRC generators supplying the specified load at bus-2007.24652 (Table-5.12 shows the variation of cumulative outage probability for different MW blocks or more of generation capacity on outage at bus-3107.3 and Fig.24 MW and the bus load is 540 MW.5.4.

5. although there is adequate reserve in the system as a whole. At some buses the LSPi is considerably low compared to other buses while at a few buses LSPi is higher than the LSPSystem. o Fig. the locational LOLP indices can be used as a basis for siting of generation capacity. which is fairly high.44 MW.5.2 0 10 15 20 25 30 35 40 45 50 55 60 3. This explains that the system reserve of 3. LOLP359 = 0. in particular. However.8 0. when a dedicated capacity of 20 MW is available at bus-359.5.15.2). It can be seen that due to the low reserve margin availability at this bus.16. of 3.
1.bus are plotted in Fig. • LSPi indices have significant variations from bus to bus.2 Cummulative Probability of Outage 1 0. some buses do not have access to that reserve.16 shows the locational LSP indices for all the buses in the system along with the system LSP for the sake of comparison.13 Cumulative Outage Probability at Bus-359 of the Ontario Based Power System having 19 SRC Generators Accountable for Supplying its Specified Load
The following observations are made from Figs. • LOLPSystem is considerably low as compared to LOLPi for several load buses. distributed generation capacities.6 0.534 MW is not uniformly accessible to all the load buses in the system. LOLP359 reduces significantly (to less than 0.44 65 0 2 3 5 Initial LOLPi Change in LOLPi
Dedicated Generation of 20MW
New LOLPi
X or more MW on Outage Cummulative Probability
Figure 5. 79
. Therefore. Therefore. o There are 14 load buses that receive a higher or almost the same level of LSP as that of the system as a whole.4 0.13 shows the cumulative outage probability curve for bus-359.5652.13-5. and hence face a low reliability condition. Fig. 5.

we obtain the LMPs through the duals of the demand-supply balance constraint.5.5. there is no congestion in the system for the load condition considered. This is because the loss model used in the OCP is approximate. Nevertheless.2 0
5. It can be observed from Fig.1.
10 100 101 103 344 359 1001 1104 1106 1301 2002 2007 2100 2106 3107 3108 3300 3301 4000 4100 4105 5003 5102 5103 5105 5135 5403 5404 5690 6400 6401 6402 6500 6501 6603 7000 7100 7102 7105 7108 7300 7302 7365 8000 8002 8103 8104 8109 8110 8112 8114 8258 9103 9112 9302 9311 Buses in the System LSPi System LSP
Figure 5.4. Also.4 0.16 Locational LSP at all Load Buses in Ontario Based Power System
81
.6 0.2.17.17 that the LMPs are almost equal at all the buses. A plot of bus-wise LMPs for the load condition considered is shown in Fig.2 1 0. this does not affect the main premise of the investigation.8 LSPi 0.4 LSP Differentiated LMPs From the simulation of the OCP for the Ontario system.

from which the locational LSP indices are determined.5. as shown in Fig.18.
5.25
20 Reverse Scaled LMPs. The concept of domains and commons and generators’ contributions to the loads is used to formulate an isolated bus configuration for each individual load bus and the LOLP index. Therefore. 5004. buses. This chapter investigates the discrepancy in LMPs with respect 83
10 100 101 103 344 359 1001 1104 1106 1301 2002 2007 2100 2106 3107 3301 4000 4100 4105 5003 5102 5103 5105 5135 5403 5404 5690 6400 6401 6402 6500 6501 6603 7000 7100 7102 7105 7108 7300 7302 7365 8000 8002 8103 8104 8109 8110 8112 8114 8258 9103 9112 9302 9311 Bus es in the Sys tem
0
Figure 5. in the order of $21/MWh. 5-Bus test power system and the 57-Bus Ontario based example. pays proportionately scaled lower LMPs or nodal prices. customers at a bus with a lower LSP level are entitled to a lower price as compared to customers located at a high LSP bus. it is rational to take into account the LSP at a bus and appropriately incorporate that into the locational prices. $/MWh
15
10
5
When the LMPs are reverse-scaled using ∆LSPi.18 LSP Differentiated Nodal Prices at Different Buses
. the customers are faced with a low LSP.5003. to elaborate the proposed approach and help develop a clear understanding of the proposed concepts. the LSP differentiated LMPs are obtained.. From the analysis of the Ontario based power system it is seen that while the LMPs at all system buses are nearly the same.5 Concluding Remarks
This chapter proposes a novel set of locational LSP indices and demonstrates how it can be used to modify the LMP to take into consideration the probability of supply received by the customers at a bus.g. Two case studies are presented viz. at several buses. It can be observed that the customers at buses with higher LSP pays a proportionately higher LMP rate while customers at the buses that are offered lower LSP level. e. Indeed. 5135 and others. is redefined based on location.

it has been shown that LSP differentiated prices can range from approximately $13/MWh at low LSP buses. In the system studies undertaken. in readiness. specific to locations.
84
. load curtailment. This work also opens up the prospect for research on reliability as a tradable feature in deregulation. without LSP consideration. to $22/MWh at high-LSP buses. and capacitor switching provisions. Such measures can include reserves. . contrary to the more or less uniform LMPs of $21/MWh at all buses. It shows that reverse scaling the LMPs with respect to the differential locational LSP indices opens a scope for effective pricing of electricity. Furthermore. the knowledge of locational LSPs can be used by the system operators to be prepared for contingency conditions and take preventive measures.to the bus-wise LSP.

without overloading the transmission system. This chapter proposes a practical approach to medium-term Transmission Reinforcement Planning (TRP) by making use of standard design practices. a new locational reliability index was proposed in Chapter-5 that can aid both in medium-term operational and planning functions in deregulated power systems.2 The Transmission Reinforcement Problem
The TRP exercise does not consider altering the right-of-way of existing corridors and hence is the fastest and most practically viable medium-term solution to alleviating the transmission system overload problem. A security coordinated medium-term maintenance-cum-production scheduling scheme was developed and presented in Chapters-3 and 4.
6. The Feasibility Set limits the type and number of reinforcement options available to the planner in selected existing corridors. Effective technical solution 4. experience and thumb-rules to construct a Feasibility Set.Chapter 6 A Practical Approach to Transmission Reinforcement Planning 1
6. 85
1
. are: 1. There are various reinforcement options available that can be opted for. Thereafter. which makes it an attractive alternative. Defer new corridor addition decisions
Based on the findings of this chapter. Some of the obvious advantages of transmission reinforcement.1 Introduction
In the previous chapters. medium-term operational and planning functions pertaining to the ISO were presented. Smaller system investment cost 2. engineering judgement. Mathematical optimization is then applied considering the Feasibility Set. to attain an optimal set of reinforcement decisions that are economical and meets the system demand in the medium-term. and implemented in a modular fashion so as to meet the budget constraints. Shorter gestation lag 3. a paper is in preparation to be submitted to the IEEE Transactions on Power Systems.

then the operational limits become active and are governed by power system stability issues. a dedicated feasibility analysis is required in order to prove their effectiveness. online dynamic security assessments and automatic voltage regulator and governor control systems [1. Such reluctance is because of the possibility of environmental degradation from forest clearances. The transmission system is characterised by the voltage level. Series compensation. To address these issues in the medium-term planning horizon (of about 5 years).71]. There are obvious limitations on a line’s power handling capacity arising from the voltage level and current carrying capacity of the transmission line.Reconductoring of transmission lines increases both the MW and thermal loading capacity of the line [49. the following TRP options are selected in order to increase the power transfer capability of existing lines in the medium-term framework of up to five years: a. In real life. Reconductoring. The technical requirements needed to be outlined and the transmission system design parameters that would be affected by exercising specific options are identified. arising as a result of lack of adequate transmission capacity. 72-74]. depending on the amount or degree of series compensation [48.Series compensation of transmission lines is known to increase the MW loading capacity of a line by up to 45%. Reconductoring can further be subcategorized as i) changing the size of the conductor only. b. land contamination. installing phase angle regulators. 71. 75]. The traditional transmission expansion planning problems involve developing new transmission corridors for power transfer. 49. which can increase the overall MW and thermal capacity by 40% and ii) duplicating or duplexing the line conductors [75]. current carrying capacity and its power handling capacity. When the transmission system as a whole is considered. 86
.To exercise the reinforcement options. etc. by small inertia generators and dispersed generation sources. installing series capacitors and /or FACTS devices. transmission reinforcement is the most practical approach to cope effectively with future demand-supply balance and persistent transmission overloading issues. propositions for such new right-of-ways are extremely difficult to implement because of the reluctance of governmental agencies to approve them. In this work. ill-effects of electromagnetic induction on general public health. The power transfer capacity of transmission lines can be affected by several factors such as changing the connections of lines at substations.

The mechanical performance parameters are its temperature rise limits and mechanical loading limits considering weather factors such air pressure and ice loading.2. The mechanical design has to be safe and capable of withstanding all weather effects along with electrical safety. the line losses in conjunction with ambient conditions may result in thermal overheating of conductors to cause annealing of the conductor material. resulting from it [76-78]. satisfying the electrical and mechanical constraints. 6. the corona effect is one of the crucial factors that is given due consideration because of the increased losses and the radio interference.between conductors. They are designed and constructed to meet the specified power handling capacity while adhering to the safety and reliability requirements and operating within the statutory and/or acceptable range of performance parameters [71].1 Line Characteristics and Line Design Aspects Transmission lines are built to transmit bulk power over a long distance.This option enhances the thermal and MW handling capacity of lines. The electrical design of a line has to take into consideration the electrical performance and its effects on other parameters. Also in case of EHV and HV transmission line design.1 Choice of Voltage Level The power transfer over a transmission line is directly proportional to the square of the voltage level of the line. and between conductor-ground
6. Voltage level upgrades. to provide a background to transmission reinforcement problems.c. Appropriate choice of the voltage level can therefore reduce line losses but would increase the line costs and the occurrence of corona effects. This reduces the mechanical strength of the line and increases the sag. To be more specific. phase-to-ground and line-line electrical clearances. d. Increasing the voltage level reduces the line current proportionately and this in turn results in a reduction of line loss. 87
.2.1. which may lead to reduction in line-to-ground clearances. The electrical design of transmission lines considers following aspects: o o o Choice of voltage level Choice of conductor Choice of insulation system . The transmission line efficiency and voltage regulation are its electrical performance parameters. New lines or circuits. A brief discussion of transmission line design from the power transfer capability view point is presented next.This option enhances both the thermal and MW capacity.

The conductor size depends on the power to be transferred over the line. and therefore it is not common to use copper conductors [1. 6. the existing voltage levels of lines in its vicinity and future plans are also to be considered.. In selecting the voltage level of a line. composite reinforced conductors.1.. are also utilized in special conditions for thermal upgrading of lines.
88
.e. ACSR conductors are preferred because of their light weight. 79]. 71.1. For high voltage lines the weight of the conductor becomes an important factor due to increased span of support towers. In such cases. which in turn depend on the size and weight of the conductor. This is the MW-Mile or kWkm principle of choice of voltage level [71]. the distance between the towers. ACSR conductors (Aluminium Conductor Steel Reinforced) and AAA conductors (All Alloy Aluminium) are the most commonly used transmission line conductors. Selection of a proper conductor configuration becomes critical with higher voltage levels. 6.3 Choice of Insulation System In overhead transmission systems. the conductors are isolated from the ground using the insulator strings. The amount of power to be transferred and the distance over which the bulk power is to be transmitted. the distance over which it is to be transmitted and the voltage level of the line selected. In many countries copper is scarce and expensive. voltage level of the transmission line has to be judiciously selected. The selection of conductor size thus depends on the losses occurring in the conductor over a year.Therefore. Copper conductors (hard drawn or stranded). The physical separation between conductors depends on the voltage level of the system and the span. after considering the economics and taking into account the cost of lines. At the support structures. The conductor configuration is the way in which conductors per phase are arranged and depends on the power handling capacity and the voltage level of the transmission line.2. and that between lines to ground. This cost rises rapidly with the voltage level. i. cost of equipment such as transformers and associated switchgear. provides a preliminary guideline for the selection of the voltage level.2 Choice of Conductor The choice of conductor involves selecting the type and the size of conductors. glass or composite material. made of porcelain. etc. Special conductors such as trapezoidal conductors.2. the insulation system generally comprises the air-gap between conductors.

transient and small-signal stability limits. 2) Line voltage limit and 3) Line operating limit [80. Over-voltages in the transmission system can cause transformer saturation or mal-function of any equipment or may even result in a fault condition.2 Factors Affecting Power Transfer Capacity of a Line The power transfer capacity of a transmission line is a function of three main parameters. there is no need of considering addition of new right-of-ways. It is assumed that in exercising these options. 72]. unsafe clearances and a shortening of life expectancy in the long-term.2. 1) Series Compensation: Connecting a capacitor in series with the transmission line results in reduction of net transfer-reactance of the transmission line. The amount of series compensation can be varied depending on the system requirement. 30% series compensation 89
.2. The series compensation options considered in the present TRP problem are: a. which in-turn increases the maximum steady-state power-transfer limit. Under-voltages are not advisable since these may lead to voltage collapse conditions. Sometimes parallel flows. Exceeding the thermal limit may result in increase in sag. the line MW loading limit can be increased by approximately 45% [48. 49. Furthermore. With 30% series compensation. 20% series compensation c. 81]. 6. 10% series compensation b. the four transmission reinforcement options mentioned earlier are elaborated to provide greater insight. 1) Line thermal limit: The allowable temperature rise limit of a transmission line is crucial because it determines the thermal expansion of the transmission line conductor. 2) Line voltage limit: Transmission systems have a specific voltage rating. 81. margins to be kept for contingency allowances and other system conditions also restrict the full utilization of a line’s thermal and MW loading capacity [80. This depends on the current carrying capacity of the conductor and the ambient conditions. the limit on the voltage magnitude directly affects the power transfer capability of the transmission line. -1) Line thermal limit. Voltages beyond the limit are unacceptable. 3) Line operating limit: The power transfer between two buses can be restricted by operating constraints such as the steady-state.3 Classification of Transmission Reinforcement Alternatives In this subsection.6. 82]. The voltages should remain within the statutory limits of this specified voltage rating.

the power handling capacity approximately gets doubled. the power transfer of the transmission line is approximately doubled. The power handling capacity is proportional to the square of the voltage level for a given distance and accordingly the increase in power handling capacity is considered in the optimization problem.3. 49. A feasibility analysis needs to be carried out after selecting the transmission reinforcement option in order to verify whether an option will be feasible technically and economically. Replacing the existing conductor by a larger size conductor – generally 40% over sizing is permitted. the power handling capacity increases by 50 percent of existing capacity. Further. this option is not considered for a 400 kV transmission line. If an existing double-circuit line is converted to a three-circuit line. There are two possibilities of reconductoring: a. by controlling the number of selection variables. 75. Duplexing is the second alternative where another conductor is added to the existing conductors [75].
6. As it is assumed that the right-of-way remains unaltered. which increases the line power transfer by 40% [48. The last measure is the voltage level upgrade of the existing transmission line. b. shunt compensation option is not considered as one of the alternatives for the transmission reinforcement because we have assumed that reactive power injection is already available at the load buses.. It is assumed that if one conductor is added to a single conductor configuration. 83]. The mathematical model of TRP will also be a MINLP problem because of the presence of non-linear load flow equations and integer variables for selection of alternatives. 3) Addition of new circuits: If a single circuit line is made double circuit. 4) Voltage level upgrade: There is a practical limit on the extent a reinforcement alternative can be exploited. which are difficult to solve for large systems.e. 83].
90
. The difficulties in solving such MINLP problems can be eliminated or regulated by controlling the size of the problem i. 75.1 Construction of TRP Feasibility Set Transmission expansion planning problems are often modelled as mixed-integer non-linear programming (MINLP) problems.3 Proposed Approach to TRP
6.2) Reconductoring: This option is meant for increasing the line power transfer capacity by line conductor reconfiguration [48.

are compared with the thermal loading obtained from the load flow run.3.2. either reconductoring or the option of adding new lines is considered. can be used to determine the actual MW and thermal loading of the lines.1. using standard design procedures and engineering judgement. a smaller set of feasible options can be arrived at. the ampacity or thermal loading limit based on conductor selection.3. either reconductoring or addition of new lines options is considered.The notion of ‘Feasibility Set’ limits the number of selection variables in the TRP problem by preidentifying the lines to be reinforced and the possible set of options that may be exercised on that line. and easy to implement. the option to add new circuits or a voltage upgrade is considered. 91
. 4) For both line thermal and MW loading in the range of 90-150%. These two can then be compared to arrive at the practical MW loading limits for all lines. depending on voltage level and the power handling capacities. A simple load flow run. various degrees of series compensation are used to increase line MW loading limits 3) If line MW loading is less than 90% and thermal loading is between 90-150%. 6. It is important to mention that by knowing the type of line and the amount of overload. are as listed below.2 Proposed Set of Rules to Alleviate Persistent Transmission Overload Persistent transmission line overloads can be eliminated by increasing the line capacity. 6.1. Optimal selection of the options from within the Feasibility Set renders the proposed approach to TRP to be practical. to determine practical line current carrying limits. 1) If the line thermal and MW overload is less than 90%. considering full-load condition. This is done using a rule-based identification of reinforcement options for each and every line preidentified for augmentation. thermal and MW loading. 5) For 150% and more thermal and MW loading of a line. the line does not need capacity reinforcement 2) If the line MW loading is 90-150% of nominal and thermal loading is less than 90%. considered in this work. The line MW loading limits are realistically determined from the line voltage rating and the line length. The transmission capacity reinforcement rules.1 Identifying Overloaded Lines Two types of line loadings are considered viz. The above proposed set of rules is shown in Table 6. These limits are used to determine the line overloads (both thermal and MW) for specified load conditions.1. as discussed in Section 6.1. In the same way.

is executed to select the reinforcement options that best reinforce the thermal and/or MW loading capacities of the overloaded lines identified. which is a mixed-integer linear program (MILP) discussed later.2.2 Overview of the Proposed TRP Approach The TRP problem is a MINLP problem and therefore it might not be possible to arrive at a feasible optimal solution for larger systems. but is expected to converge fast. 6.1. to identify any further existing transmission overloads. because of the nature of the problem itself. presented in this sub-section is a decomposition-based approach in which the TRP problem is split into two sub-problems and solved sequentially and iteratively.3. Two solution approaches are proposed in this work. This scheme is iterative in nature. In the proposed approach.3. while minimizing the investment cost objective. the reinforcement options are identified and the Feasibility Set for the overloaded lines is developed using Table 6. the Transmission Reinforcement Selection (TRS) model.
92
. to arrive at a solution (Fig. Once the Base-OPF yields a solution with no transmission overloads. the optimal solution of reinforcement options is obtained. first a Base-OPF is executed to identify the lines that have a thermal or MW overload. to determine the feasible selection of reinforcement options. The optimal selection of reinforcement options are incorporated in the power system configuration with new upgrades and the revised system is executed for Base-OPF run.Table 6. Thereafter. 6.1).1 Decomposition Approach to TRP The first approach. Once the lines are identified and the Feasibility Set is available.1 Allotting Reinforcement Options Based on the Type and Amount of Line Overload % MW Loading % Thermal Loading ≤ 90% 90-150% ≥ 150 ≤ 90% No Reinforcement Reconductoring Duplexing only New Line Additions Voltage upgrade 90-150% Series Compensation Reconductoring New Line Addition Voltage Upgrade Duplexing only New Line Additions Voltage upgrade ≥ 150% New line addition Voltage Upgrade Duplexing only New Line Additions Voltage upgrade Duplexing only New Line Additions Voltage upgrade
6.

j
OL Pi .Input.2 Unified Approach In this approach. j Max Pi .2. j Max I i. is executed to select the reinforcement options that best reinforce the thermal and/or MW loading capacities of the overloaded lines identified. while minimizing the investment cost objective.1 Decomposition Approach to TRP
6. subject to the line security constraints. 93
. the Security-Constrained Composite Transmission Reinforcement Selection (SCC-TRS) model (discussed later). j
Revise System Configuration with new upgrades
Overloaded Lines
Overload exists? NO
Line Flows
YES Segregate lines as per the type & amount of overload
Optimal Selection
Construct Feasibility Set Selected reinforcement options Feasibility Set Solve TRS Model to obtain optimal selection of transmission reinforcement
Figure 6. j =
I i. Once the overloaded lines are identified and the Feasibility Set is constructed. which is MINLP in nature. which is a MINLP problem.System Data
Base . j =
Pi . the comprehensive TRP problem. is considered where the imposition of line constraints and the reinforcement option selections are simultaneously implemented so as to arrive at a cost effective solution that best meets the system requirements.Optimal Power Flow Line Flows Determine the overloaded lines
Selected reinforcement options
OL I i.3.

j OL Pi . j
Max I i. j
Overloaded Lines
Overload exists?
NO
No Reinforcement required
YES Segregate lines as per the type & amount of overload
Construct Feasibility Set Feasibility Set
Solve Security Constrained Composite TRS Model
Optimal selection of Reinforcement options
Figure 6. the size of the problem is strictly limited and can be easily solved using available MINLP solvers. 6.System Data
Base .Optimal Power Flow Line Flows Determine the overloaded lines
OL I i.2 Unified Approach to TRP
94
. j = Max Pi .Although this is a unified approach dealing with a MINLP problem. j Pi . j =
I i.
Input. because of the presence of the Feasibility Set. The overall TRP solution method using the unified approach is described in the Fig.2.

25)
Z i. o ≤ 1
(6.5. j . The equation (6.j. kV MW Capacity. New line addition d.24) (6.4. 6.5 Case Study – CIGRE 32 Bus Test System
6.j. Equation (6. MW Thermal Capacity.2 Line MW and Thermal Capacities Line Voltage Level. 49.1 System Data
The proposed approach to TRP is carried out considering the CIGRE 32 bus test system (Fig.j. The detailed data for this test system is provided in the Appendices.o = 0
6.o = 0 ∀ ΔPCap i.2 [1. The transmission line reinforcement options considered for the present studies are as follows: a. are selected as shown in Table 6. only one reinforcement option has to be selected.4 Feasibility Constraints For a line that requires capacity addition. A 132 300 450 230 500 700 400 1200 1400
99
.o = 0 and ΔICap i.24) limits the option selection for a line to 1.6. 48.
No o
∑ Z i. 71-82]: Table 6.3. Series compensation b. Reconductoring c. Voltage level upgrade The line thermal and MW power handling capacities considered in these work.25) restricts the range of the binary selection variable to the lines within the Feasibility Set.3) [84] to examine and compare the performance of the Decomposition Approach with the Unified Approach.

5. 2) 3) No right-of-way addition or modification is required to implement the reinforcement options. the proposed approaches are generic enough to consider specific line lengths.2 Cost Data 6. MW loading and thermal loading of a line are considered separately. However.Figure 6. This assumption is made because of lack of such information on the CIGRE 32-Bus Test System.1 Assumptions for Cost and Reinforcement Option Considerations 1) Transmission lines are assumed to be 200 miles long for the purpose of estimating existing line costs.5.3 CIGRE 32-Bus Test System [84]
6.
100
.2.

101
. The transmission line costs vary significantly. and lead time impacts on projected cost.3.3 also shows the respective option codes which are later used to discuss the results. Therefore. The Table 6.. for overload mitigation and also allows to either choose a modular reinforcement option or to help schedule the selected alternatives over a specified time-frame.2 [1. This provides an opportunity to the planner to optimize within the limited standard design options available. for example. 49. For the work presented in this chapter the costs for 138kV. 49]. VNEW = 2 for 132 kV line and VNEW= 4 for 230 kV line.1. etc.5. to define the amount of reinforcement and the alternatives available within each option. Table 6. such as land acquisition costs.3 Reinforcement Option Sub-categories and Respective Codes Options Series Compensation Reconductoring New Line Addition Sub-categories 10% Compensation 20% Compensation 30% Compensation Resizing Duplexing Single Circuit Addition Double Circuit Addition One Level Upgrade Only Option Codes S_1_V S_2_V S_3_V R_S_V R_D_V N_1_V N_2_V V_VNEW_V
Voltage Level Upgrade (Not considered for 400 kV lines) Note: V in Option Code stands for voltage level of a line. [1. labour cost. the costs of existing transmission are estimated and then appropriate percentage of various transmission line costs are allotted to specific reinforcement options for a line type.2. due to factors other than the line capacity. the conductor configuration is assumed to remain constant for a specific voltage level. For all transmission lines. 6.4)
Thermal loading of a line is approximated as ampacity limit of the conductor. other regulations.
5)
The four reinforcement options are further sub-categorized as shown in the Table 6.2 Cost Parameters of a Transmission Line and Reinforcement Alternatives In order to determine the cost parameters of all the transmission reinforcement alternatives. The transmission line capacities are also considered as specified in Table 6. 230kV and 400 kV lines are estimated considering the assumptions stated in Section-6. V=2 for 230 kV line and V=4 for 400 kV line. 71-82]. 48. V=1 for 132 kV line.5. S_1_1 denotes 10% series compensation in a 132kV line and R_S_2 denotes a conductor resizing in a 230 kV line.2.

and the outage cost of the transmission line during commissioning.3 Result and Discussions 6.3. 6. the identified lines and suitable reinforcement options are together used to construct the Feasibility Set for the TRP problem. The overloaded lines identified are segregated on the basis of the amount of thermal overload or MW overload or both thermal and MW overload.•
The cost of the series compensation depends on the degree of compensation and the voltage rating of the transmission line to be compensated. as shown in Table 6. which implies a 3% annual load growth. Lines with lower MW loading and high thermal overloading require thermal up-rating of the transmission lines.4.
102
. For example.5. The other major cost for series compensation is the cost associated with the terminal station. the incremental MW power handling capacity reduces proportionately. Capacitor costs are estimated to be in the range of 10-15% of the cost of new lines [49. The applicability of various reinforcement options to alleviate any type of overload in each “identified” line was determined. Re-sizing increases line power handling capacity by 40%. lines with thermal loading less than 90% and the MW loading in the range of 90-150% requires the series compensation option in order to increase the MW loading capacity of these lines. Generally 30% series compensation results in 45-50% rise in the MW power handling capacity [48.5.
•
New line or circuit addition and voltage upgrade costs are derived from the estimated costs of existing transmission lines for various voltage levels and their differentials in case of voltage upgrade.1 Determination of Feasibility Set The Base OPF simulations are used to compute the line thermal and MW overloads assuming 15% system load increase over a five year span.
All the estimated costs corresponding to the reinforcement options are annualized considering a period of 25 years and a discount rate of 10%.
•
The cost of resizing option is approximated to be 40% of the new line cost. Finally. For 10% and 20% series compensation. The cost of duplexing option is approximated to be 70% of the cost of a new line. 50]. 49] of the line. while the capacity increase achieved from the duplexing option is 80% of line capacity [75].

20% or 30% of compensation.6 displays the corresponding reinforcement costs by series compensation for line 4011-4021 in rows S_1_4. The degree of series compensation can be varied by. 10%. series compensation can provide the increase in line MW loading capability. with proportionate increase in MW loading (Table 6.Table 6. S_2_4 and S_3_4 respectively.4 Overload Paths for a 15% System Load Growth
MW loading Thermal loading ≤ 90% ≤ 90% 90% – 150% ≥ 150%
None
90% – 150% ≥ 150%
1022-4022 None
4011-4021 4031-4032 4062-62 1043-1041 4044-1044 4045-1045 1045-1041 4031-4041 1013-1011 1044-1043 None
None
4042-42 4022-4031 None
Table 6.
103
. These two tables along with another table (not shown here) representing thermal capacity increment for various reinforcement options will comprise the Feasibility Set for the TRP problem under consideration.6 presents the corresponding annualized costs of different reinforcement options.5 presents the capacity increments and Table 6. and it does not require thermal upgrade. say. Table 6. Therefore. line 4011-4021 has only MW overloading. For example.5).

kV) are provided with 20% series compensation, one line (4031-4041, 400kV) is allotted the reinforcement option of conductor re-sizing while one 400 kV line (4022-4031) is advised the option of adding one more circuit to alleviate thermal and MW overloading. Figure 6.4 shows the 32 bus CIGRE system with the options suggested as an outcome of the Decomposition Approach to TRP problem. Table 6.7 TRP Solution using Decomposition Approach
S_2_1 4031.4041 4062.62 1043.1041 4022.4031 1045.1041 1 1 1 1 R_S_4 1 N_1_4

It is observed from Table 6.8 that four lines (4011-4021, 4062-62, 1043-1041 and 1045-1041) are provided with different degrees of series compensation options and one line (4022-4031, 400kV) is advised the option of adding one more circuit for alleviating thermal and MW overloading. Figure 6.5 shows the 32-bus CIGRE system with the options suggested as an outcome of the Unified Approach to TRP problem.

107

It is observed that the total investment cost resulting from the Decomposition Approach is 22.Figure 6.12%. which is higher by 16.5 Reinforcement Options Selected in the Unified Approach
The investment costs obtained from both approaches are presented in Table 6. This is because of the inherent inability of the Decomposition Approach to capture the interactive overloads. 108
.25 M$ accrued in the Unified Approach. than the investment cost of 19.95 M$.9.

The decomposition approach is solved on a standard Intel Xeon processor with 3 GB RAM.10 Computational Details of Optimization Problems
Event Equation Blocks Variable Blocks Single equations Single variables Non zero elements Discrete variables Model Generation time(sec) Model Execution time (sec) Decomposition Approach Base OPF TRS 10 3 8 2 3.737 43. Table-4. Table 6.187 0.385 70 0. the CPLEX solver in GAMS [70] is used to solve the TRP problem using Decomposition Approach.157 0. However. the Decomposition Approach and the Unified Approach.241
6.7 provides the details of the size of the mathematical models. On other hand the Unified Approach is able to solve the comprehensive TRP problem directly using the MINLP solvers. the Unified Approach is easily solved by the commercially available MINLP solvers.954 53. because of the reduced problem size achieved with the help of the Feasibility Set and also achieves a lower total investment cost. easily.6 Concluding Remarks
This chapter presents a new approach to address the medium-term TRP problem by using practical judgment and engineering experience to simplify the computational aspects via the notion of Feasibility Set. the total investment cost is higher.687 3.568 35.95 19.141 0.1400
The computational burden of the Unified Approach is higher than the Decomposition Approach due to the obvious differences in the nature of these problems.302 5.234 Unified Approach SCC-TRS 17 14 13. while SBB solver on NEOS [85] is used to solve the TRP problem using Unified Approach.184 35.174 70 0.Table 6. The Feasibility Set helps reduce the problem size and hence optimal solution is easily obtained even when the TRP problem is modeled as a MINLP problem. Two approaches to solution of the MINLP problem are examined.650 1. In this work.9 Investment Costs in M$ Obtained from both TRP Solution Methods
Decomposed Approach Unified Approach 22.
109
. It is seen that although the Decomposition Approach simplifies the computation.219 0.

Chapter 1 of the thesis introduces to the issues in medium-term operations and planning in restructured electricity market environment. The chapter discusses the medium-term planning issues with specific focus on the “insufficiently attended” transmission reinforcement activity.Chapter 7 Conclusions
7. The chapter finally discusses the objectives set for this thesis. These issues are either discovered or have surfaced due to electricity sector deregulation or generated as a result of a unique thoughtprocess emerged because of the restructuring phenomenon. Chapter 2 discusses the pertinent medium-term operations issues of production and maintenance scheduling in power systems and brings out the changed paradigm of operation and need for coordination of these functions by the ISO in the context of deregulation. It briefs the present state of Ontario’s electricity sector and outlines the challenges faced by Ontario electricity market. locational reliability and the TRP problems in order to develop an understanding of the issues and the state-of-art in the research in these significant subjects of medium-term operations and planning in power systems. but calls for maintenance schedules from individual gencos. Based on the information on bus-wise unserved energy. The research work focuses on diverse but interlinked issues in medium-term power system operations and planning. to ISO. of a new approach to security coordinated maintenance scheduling in deregulation. the ISO does not generate a maintenance schedule by itself. Chapter 3 presents the mathematical formulation and details. which can provide critical information regarding the load serving probability. The maintenance schedules plans. when incorporated in a medium-term security constrained production scheduling model can result in unserved energy at one or more buses. the ISO generates 110
. Thereafter the Chapter provides insight in to the motivation that inspired this research work. A modest attempt is made in this chapter to review the literature on production-cum-maintenance scheduling.1 Summary and Conclusions
This thesis explores different aspects of medium-term operations and planning of power systems in deregulated electricity market environment. Maintenance scheduling of generating units is an important medium-term operations planning activity that reduces the risk of capacity outages. It further charts the need for a locational reliability index. In this novel framework.

The methodology is applied to a 5-bus test system and the reduced representative Ontario test system. Chapter 4 presents a comprehensive case study for a large 3-utility. understandable and simple. The proposed scheme exploits the concept of commons and domains to derive a novel factor to allocate the unserved energy at a bus to a set of generators responsible. Detailed model simulation results are presented in this Chapter to demonstrate the application of the proposed scheme with insight on the coordination process. efficient and can be applied to practical power systems. logical. unless it is absolutely important from system security considerations. the knowledge of locational LSPs can be used by the system operators to be prepared for contingency conditions and take preventive measures. Two modelling approaches to solve the TRP problem are presented. and tries to retain these schedules as far as possible. A new LSP index based on locational LOLP indices are proposed and the mathematical approach to compute these locational reliability indices is presented. Iterations between the gencos and ISO continue until the coordination program has converged. Chapter 5 investigates the discrepancy in LMPs with respect to the bus-wise LSP. The proposed approach is easier to implement and reduces the size of the problem and seeks to attain optimal solution within the feasibility range.corrective signals for the genco(s). specific to locations. The scheme is very efficient and converges within five iterations and has the advantage of being fair. determined from locational LOLP indices. 37-generator system that approximately represent the Ontario power system. Furthermore. Chapter 6 presents a new approach to medium-term TRP which takes into account engineering judgment and experience to develop a Feasibility Set of transmission reinforcement options. and directs them to alter their maintenance schedules in specific periods and re-submit. and capacitor switching provisions. The coordination scheme is based on individual genco’s accountability to unserved energy at a bus. to make the approach easy to understand and verify its applicability to a practical sized system. and there is no unserved energy at any period in the system. It shows that reverse scaling the LMPs with respect to the differential locational LSP indices opens a scope for effective pricing of electricity. This work also opens up the prospect for research on reliability as a tradable feature in deregulation. Such measures can include reserves. It also takes into consideration the gencos’ individual maintenance schedules. load curtailment. The Decomposition Approach focuses on the cost minimization of identified 111
. The proposed scheme is computationally simple. Chapter 5 focuses on locational reliability indices and introduces the concept of reliability differentiated pricing in the context of competitive electricity markets. to modify them.

6. The computational burden on ISO is also reduced tremendously as the proposed coordination scheme does not require the ISO to compute the maintenance schedules for all gencos. Its solution is a feasible solution. and provides better solution as compared to the Decomposition Approach. 7. and tries to maintain these schedules as far as possible. A novel factor is introduced to allocate the unserved energy to the gencos who are accountable for not serving the energy. The Unified Approach does take interactive overloads into account. 5. and locational LSP indices are proposed. A novel concept of locational reliability indices is put forward in this thesis and the locational LOLP. 2. The proposed Feasibility Set helps reduce the problem size and 112
.reinforcement options for the congested lines. A new approach is presented in the thesis to address the medium-term TRP problem by using practical judgment and engineering experience to simplify the computational aspects via the notion of Feasibility Set. logical. The coordinated maintenance scheduling scheme arrives at an optimal medium-term production-cum-maintenance schedule that takes into account all relevant system constraints. but as the interactive overloads are not taken into considerations. is proposed. unless it is absolutely critical from system security considerations to request for their modifications. 4. proposed and utilized to derive a methodology of computing the locational LOLP indices and hence. The concept of reliability differentiated pricing is proposed in this thesis and a simple reverse scaling approach based on locational LSP indices. as critical signals. A novel security coordination scheme is proposed in the thesis for the medium-term maintenance scheduling problem in deregulation that iterates between the multiple GMS Programs and the OCP using gencos’ contribution to unserved energy.2 Main Contributions of the Thesis
1. An innovative concept of Isolated Bus Representation is developed.
7. understandable and simple. The scheme is fair. It takes into consideration the gencos’ individual schedules. based on their contribution to a load at a bus and the capacity of genco on maintenance. to obtain reliability differentiated LMPs. the locational LSP indices. 8. 3. The proposed scheme is very efficient and converges in five iterations. to arrive at. an iterative solution strategy has to be formulated considering the verification after each step of selection of reinforcement options for congested lines.

load demand and other parameters that are subject to variations. 1. 2.hence optimal solution is easily obtained even when TRP problem is modeled as a MINLP problem.3 Scope for Future Work
On the basis of the research work reported in this thesis. This method will provide a comparison of performance of the method of commons and domains presented in this thesis. 9. may be incorporated to make it more effective and 113
. 4. because of the reduced problem size with the help of Feasibility Set and also achieves a lower total investment cost. Apply a stochastic programming approach to address the uncertainties associated with price.
7. in the mediumterm security coordinated maintenance scheduling problem. A prioritizing approach can be exploited to develop a comprehensive iterative algorithm. the following directions may be pursued for future research work. and hence obtain the expected medium-term solution. in the verification stage. 5. Furthermore. 3. so that the optimal solution on the convergence of algorithm is guaranteed. which are realistically determined. fuel costs. The Decomposition Approach is a sequential approach that solves a MILP problem to select the feasible solution while trying to overcome the thermal and/or MW capacity deficit observed from Base OPF. Apply a sensitivity based approach using information provided by Langrangian multipliers to identify the contributions of gencos to the loads and solve the medium-term security coordinated maintenance scheduling problem. Two different solution approaches to solve the MINLP TRP problem are proposed. The Isolated Bus Representation concept can be further developed to a matured state and there is scope for exploring newer methods of computing locational reliability indices. Whereas the Unified Approach is able to solve the comprehensive TRP problem directly using the MINLP solvers. System security constraints are incorporated in terms of line MW and thermal overload limits. The proposed Decomposition Approach to TRP can be made more robust to take into consideration the interactive overloads without losing its simplicity and the MILP nature of the model. specialized reliability differentiated pricing mechanism can be developed considering social welfare and other electricity market economic aspects. The Decomposition Approach and the Unified Approach. easily. The proposed Unified Approach to TRP may also be modified and other contingency and transient analysis.

practically applicable TRP solution Approach. risk management. and uncertainties may be considered to attain a
sophisticated.
Further.
114
.robust.